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Solving Rational Equations
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0074.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
An equati= on or relation expressed using fractions may always be restated in = a way without using fractions.
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0075.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
=
=
We do thi= s by multiplying the LCD to the both sides of the equation, distribute it to each term to clear all the denominat= ors.
Solving Rational Equations
An equati= on or relation expressed using fractions may always be restated in = a way without using fractions.
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0076.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Example A. Suppose the value of 3/4 of an apple is the same = as the value of 1/2 of a banana with 1/3 of a cantaloupe, restate this relation in whole values.
=
=
We do thi= s by multiplying the LCD to the both sides of the equation, distribute it to each term to clear all the denominat= ors.
Solving Rational Equations
An equati= on or relation expressed using fractions may always be restated in = a way without using fractions.
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0077.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Example A. Suppose the value of 3/4 of an apple is the same = as the value of 1/2 of a banana with 1/3 of a cantaloupe, restate this relation in whole values.
=
=
We do thi= s by multiplying the LCD to the both sides of the equation, distribute it to each term to clear all the denominat= ors.
Solving Rational Equations
An equati= on or relation expressed using fractions may always be restated in = a way without using fractions.
Let A =3D apple, B =3D banana, and C =3D cantaloupe
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0078.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Example A. Suppose the value of 3/4 of an apple is the same = as the value of 1/2 of a banana with 1/3 of a cantaloupe, restate this relation in whole values.
=
=
We do thi= s by multiplying the LCD to the both sides of the equation, distribute it to each term to clear all the denominat= ors.
Solving Rational Equations
An equati= on or relation expressed using fractions may always be restated in = a way without using fractions.
Let A = =3D apple, B =3D banana, and C =3D cantaloupe
The rela= tion is
3
4
A
1
2
B +
=3D
1
3
C
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0078_image001.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0078_image002.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0078_image003.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0066.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Example A. Suppose the value of 3/4 of an apple is the same = as the value of 1/2 of a banana with 1/3 of a cantaloupe, restate this relation in whole values.
=
=
We do thi= s by multiplying the LCD to the both sides of the equation, distribute it to each term to clear all the denominat= ors.
Solving Rational Equations
An equati= on or relation expressed using fractions may always be restated in = a way without using fractions.
The LCD =3D12, multiply it to both sides.
3
4
A
1
2
B +
=3D
1
3
C
Let A = =3D apple, B =3D banana, and C =3D cantaloupe
The rela= tion is
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0079.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Example A. Suppose the value of 3/4 of an apple is the same = as the value of 1/2 of a banana with 1/3 of a cantaloupe, restate this relation in whole values.
=
=
We do thi= s by multiplying the LCD to the both sides of the equation, distribute it to each term to clear all the denominat= ors.
Solving Rational Equations
An equati= on or relation expressed using fractions may always be restated in = a way without using fractions.
The LCD =3D12, multiply it to both sides.
3
4
A
1
2
B +
=3D
3
4
A
1
2
B +
=3D
(
)
1
3
C
1
3
C
 * 12 <= span style=3D'font-size:133%;mso-special-format:lastCR;display:none'>
Let A = =3D apple, B =3D banana, and C =3D cantaloupe
The rela= tion is
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0079_image004.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0079_image005.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0079_image006.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAN AAEAgAAAAAAAAAIDjI9XADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0079_image007.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAN AAEAgAAAAAAAAAIDjI9XADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0079_image008.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0079_image009.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0080.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Example A. Suppose the value of 3/4 of an apple is the same = as the value of 1/2 of a banana with 1/3 of a cantaloupe, restate this relation in whole values.
=
=
We do thi= s by multiplying the LCD to the both sides of the equation, distribute it to each term to clear all the denominat= ors.
Solving Rational Equations
An equati= on or relation expressed using fractions may always be restated in = a way without using fractions.
The LCD =3D12, multiply it to both sides.
3
4
A
1
2
B +
=3D
3
4
A
1
2
B +
=3D
(
)
1
3
C
1
3
C
 * 12 <= span style=3D'font-size:133%;mso-special-format:lastCR;display:none'>
Distribute it to each term.
Let A = =3D apple, B =3D banana, and C =3D cantaloupe
The rela= tion is
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0080_image010.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0080_image011.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0080_image012.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAN AAEAgAAAAAAAAAIDjI9XADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0080_image013.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAN AAEAgAAAAAAAAAIDjI9XADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0080_image014.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0080_image015.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0081.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Example A. Suppose the value of 3/4 of an apple is the same = as the value of 1/2 of a banana with 1/3 of a cantaloupe, restate this relation in whole values.
=
=
We do thi= s by multiplying the LCD to the both sides of the equation, distribute it to each term to clear all the denominat= ors.
Solving Rational Equations
An equati= on or relation expressed using fractions may always be restated in = a way without using fractions.
The LCD =3D12, multiply it to both sides.
3
4
A
1
2
B +
=3D
3
4
A
1
2
B +
=3D
(
)
1
3
C
1
3
C
 * 12 <= span style=3D'font-size:133%;mso-special-format:lastCR;display:none'>
Distribute it to each term.
3
Let A = =3D apple, B =3D banana, and C =3D cantaloupe
The rela= tion is
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0081_image016.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0081_image017.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0081_image018.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAN AAEAgAAAAAAAAAIDjI9XADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0081_image019.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAN AAEAgAAAAAAAAAIDjI9XADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0081_image020.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0081_image021.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0081_image022.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAoAgAAAAAAAAAIThI8XybCtHnTTBAlxu5VW/nVGAQA7 ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0082.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Example A. Suppose the value of 3/4 of an apple is the same = as the value of 1/2 of a banana with 1/3 of a cantaloupe, restate this relation in whole values.
=
=
We do thi= s by multiplying the LCD to the both sides of the equation, distribute it to each term to clear all the denominat= ors.
Solving Rational Equations
An equati= on or relation expressed using fractions may always be restated in = a way without using fractions.
The LCD =3D12, multiply it to both sides.
3
4
A
1
2
B +
=3D
3
4
A
1
2
B +
=3D
(
)
1
3
C
1
3
C
 * 12 <= span style=3D'font-size:133%;mso-special-format:lastCR;display:none'>
Distribute it to each term.
3
6
4
Let A = =3D apple, B =3D banana, and C =3D cantaloupe
The rela= tion is
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0082_image023.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0082_image024.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0082_image025.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAN AAEAgAAAAAAAAAIDjI9XADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0082_image026.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAN AAEAgAAAAAAAAAIDjI9XADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0082_image027.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0082_image028.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0082_image029.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAoAgAAAAAAAAAIThI8XybCtHnTTBAlxu5VW/nVGAQA7 ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0082_image030.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAP AAoAgAAAAAAAAAIShI8YyRDbVFRwOmsevlj37WEFADs= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0082_image031.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAoAgAAAAAAAAAIThI8XybGMHjRuKkvl1LBi3mFHAQA7 ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0083.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Example A. Suppose the value of 3/4 of an apple is the same = as the value of 1/2 of a banana with 1/3 of a cantaloupe, restate this relation in whole values.
=
=
We do thi= s by multiplying the LCD to the both sides of the equation, distribute it to each term to clear all the denominat= ors.
Solving Rational Equations
An equati= on or relation expressed using fractions may always be restated in = a way without using fractions.
The LCD =3D12, multiply it to both sides.
3
4
A
1
2
B +
=3D
3
4
A
1
2
B +
=3D
(
)
1
3
C
1
3
C
 * 12 <= span style=3D'font-size:133%;mso-special-format:lastCR;display:none'>
Distribute it to each term.
3
6
4
9A =3D 6B + 4C
Let A = =3D apple, B =3D banana, and C =3D cantaloupe
The rela= tion is
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Example A. Suppose the value of 3/4 of an apple is the same = as the value of 1/2 of a banana with 1/3 of a cantaloupe, restate this relation in whole values.
=
=
We do thi= s by multiplying the LCD to the both sides of the equation, distribute it to each term to clear all the denominat= ors.
Solving Rational Equations
An equati= on or relation expressed using fractions may always be restated in = a way without using fractions.
The LCD =3D12, multiply it to both sides.
3
4
A
1
2
B +
=3D
3
4
A
1
2
B +
=3D
(
)
1
3
C
1
3
C
 * 12 <= span style=3D'font-size:133%;mso-special-format:lastCR;display:none'>
Distribute it to each term.
3
6
4
9A =3D 6B + 4C
Hence 9 apples is the same as 6 banana with 4 cantaloupe.
Let A = =3D apple, B =3D banana, and C =3D cantaloupe
The rela= tion is
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0084_image041.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0084_image042.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0084_image043.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAN AAEAgAAAAAAAAAIDjI9XADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0084_image044.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAN AAEAgAAAAAAAAAIDjI9XADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0084_image045.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0084_image046.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0084_image047.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAoAgAAAAAAAAAIThI8XybCtHnTTBAlxu5VW/nVGAQA7 ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0084_image048.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAP AAoAgAAAAAAAAAIShI8YyRDbVFRwOmsevlj37WEFADs= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0084_image049.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAoAgAAAAAAAAAIThI8XybGMHjRuKkvl1LBi3mFHAQA7 ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0067.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
To solve = an equation with fractional terms, we first clear the fractions= by multiplying both sides by the LCD.
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0085.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
To solve = an equation with fractional terms, we first clear the fractions= by multiplying both sides by the LCD.
Example B.  Solve
3
x – 1
=3D
6
x + 2
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0085_image050.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAp AAEAgAAAAAAAAAIFjI+py1kAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0085_image051.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAo AAEAgAAAAAAAAAIFjI+py1gAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0086.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
To solve = an equation with fractional terms, we first clear the fractions= by multiplying both sides by the LCD.
Example B.  Solve
3
x – 1
=3D
6
x + 2
Multiply both sides by the LCD =3D (x – 1)(x + 2)
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0086_image052.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAp AAEAgAAAAAAAAAIFjI+py1kAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0086_image053.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAo AAEAgAAAAAAAAAIFjI+py1gAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0087.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
To solve = an equation with fractional terms, we first clear the fractions= by multiplying both sides by the LCD.
Example B.  Solve
3
x – 1
=3D
6
x + 2
Multiply both sides by the LCD =3D (x – 1)(x + 2)
3
x – 1
=3D
6
x + 2
(
) *
(x – 1)(x + 2)
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0087_image054.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAp AAEAgAAAAAAAAAIFjI+py1kAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0087_image055.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAo AAEAgAAAAAAAAAIFjI+py1gAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0087_image056.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAp AAEAgAAAAAAAAAIFjI+py1kAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0087_image057.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAp AAEAgAAAAAAAAAIFjI+py1kAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0068.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
To solve = an equation with fractional terms, we first clear the fractions= by multiplying both sides by the LCD.
Example B.  Solve
3
x – 1
=3D
6
x + 2
Multiply both sides by the LCD =3D (x – 1)(x + 2)
3
x – 1
=3D
6
x + 2
(
) *
(x – 1)(x + 2)
(x + 2)
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0088.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
To solve = an equation with fractional terms, we first clear the fractions= by multiplying both sides by the LCD.
Example B.  Solve
3
x – 1
=3D
6
x + 2
Multiply both sides by the LCD =3D (x – 1)(x + 2)
3
x – 1
=3D
6
x + 2
(
) *
(x – 1)(x + 2)
(x – 1) =
(x + 2)
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0088_image058.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAp AAEAgAAAAAAAAAIFjI+py1kAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0088_image059.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAo AAEAgAAAAAAAAAIFjI+py1gAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0088_image060.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAp AAEAgAAAAAAAAAIFjI+py1kAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0088_image061.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAp AAEAgAAAAAAAAAIFjI+py1kAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0088_image062.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAt AAoAgAAAAAAAAAIghI+pyxvRomSvzhvrw1xp2IXAJ4ZkyZ3opa5S675bLBYAOx== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0088_image063.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhXwAQAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQBe AA4AgAAAAAAAAAI5hI+py+0PYZgh2oszo1z7DxocFZbmM07nyoppC4epGtfZbOcXrvcO7wsmgMIi sRg8InvKJbPjjB4KADs= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0088_image064.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAs AAoAgAAAAAAAAAIghI+pyxsNIwuUytuqxRzp14VfKGpkN55Yqkps625wWAAAOw== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0089.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
3(x + 2) =3D 6( x – 1)
Solving Rational Equations
To solve = an equation with fractional terms, we first clear the fractions= by multiplying both sides by the LCD.
Example B.  Solve
3
x – 1
=3D
6
x + 2
Multiply both sides by the LCD =3D (x – 1)(x + 2)
3
x – 1
=3D
6
x + 2
(
) *
(x – 1)(x + 2)
(x – 1) =
(x + 2)
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3(x + 2)= =3D 6( x – 1)
  3x + 6 =3D 6x – 6
Solving Rational Equations
To solve = an equation with fractional terms, we first clear the fractions= by multiplying both sides by the LCD.
Example B.  Solve
3
x – 1
=3D
6
x + 2
Multiply both sides by the LCD =3D (x – 1)(x + 2)
3
x – 1
=3D
6
x + 2
(
) *
(x – 1)(x + 2)
(x – 1) =
(x + 2)
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0090_image072.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAp AAEAgAAAAAAAAAIFjI+py1kAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0090_image073.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAo AAEAgAAAAAAAAAIFjI+py1gAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0090_image074.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAp AAEAgAAAAAAAAAIFjI+py1kAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0090_image075.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAp AAEAgAAAAAAAAAIFjI+py1kAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0090_image076.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAt AAoAgAAAAAAAAAIghI+pyxvRomSvzhvrw1xp2IXAJ4ZkyZ3opa5S675bLBYAOx== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0090_image077.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhXwAQAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQBe AA4AgAAAAAAAAAI5hI+py+0PYZgh2oszo1z7DxocFZbmM07nyoppC4epGtfZbOcXrvcO7wsmgMIi sRg8InvKJbPjjB4KADs= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0090_image078.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAs AAoAgAAAAAAAAAIghI+pyxsNIwuUytuqxRzp14VfKGpkN55Yqkps625wWAAAOw== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0091.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
3(x + 2)= =3D 6( x – 1)
  3x + 6 =3D 6x – 6
    6 + 6 =3D 6x – = 3x
Solving Rational Equations
To solve = an equation with fractional terms, we first clear the fractions= by multiplying both sides by the LCD.
Example B.  Solve
3
x – 1
=3D
6
x + 2
Multiply both sides by the LCD =3D (x – 1)(x + 2)
3
x – 1
=3D
6
x + 2
(
) *
(x – 1)(x + 2)
(x – 1) =
(x + 2)
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0091_image079.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAp AAEAgAAAAAAAAAIFjI+py1kAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0091_image080.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAo AAEAgAAAAAAAAAIFjI+py1gAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0091_image081.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAp AAEAgAAAAAAAAAIFjI+py1kAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0091_image082.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAp AAEAgAAAAAAAAAIFjI+py1kAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0091_image083.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAt AAoAgAAAAAAAAAIghI+pyxvRomSvzhvrw1xp2IXAJ4ZkyZ3opa5S675bLBYAOx== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0091_image084.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhXwAQAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQBe AA4AgAAAAAAAAAI5hI+py+0PYZgh2oszo1z7DxocFZbmM07nyoppC4epGtfZbOcXrvcO7wsmgMIi sRg8InvKJbPjjB4KADs= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0091_image085.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAs AAoAgAAAAAAAAAIghI+pyxsNIwuUytuqxRzp14VfKGpkN55Yqkps625wWAAAOw== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0092.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
3(x + 2)= =3D 6( x – 1)
  3x + 6 =3D 6x – 6
    6 + 6 =3D 6x – = 3x
        12 =3D 3x
        = ;  4 =3D x 
Solving Rational Equations
To solve = an equation with fractional terms, we first clear the fractions= by multiplying both sides by the LCD.
Example B.  Solve
3
x – 1
=3D
6
x + 2
Multiply both sides by the LCD =3D (x – 1)(x + 2)
3
x – 1
=3D
6
x + 2
(
) *
(x – 1)(x + 2)
(x – 1) =
(x + 2)
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0092_image086.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAp AAEAgAAAAAAAAAIFjI+py1kAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0092_image087.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAo AAEAgAAAAAAAAAIFjI+py1gAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0092_image088.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAp AAEAgAAAAAAAAAIFjI+py1kAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0092_image089.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAp AAEAgAAAAAAAAAIFjI+py1kAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0092_image090.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAt AAoAgAAAAAAAAAIghI+pyxvRomSvzhvrw1xp2IXAJ4ZkyZ3opa5S675bLBYAOx== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0092_image091.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhXwAQAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQBe AA4AgAAAAAAAAAI5hI+py+0PYZgh2oszo1z7DxocFZbmM07nyoppC4epGtfZbOcXrvcO7wsmgMIi sRg8InvKJbPjjB4KADs= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0092_image092.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAs AAoAgAAAAAAAAAIghI+pyxsNIwuUytuqxRzp14VfKGpkN55Yqkps625wWAAAOw== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0093.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
3(x + 2)= =3D 6( x – 1)
  3x + 6 =3D 6x – 6
    6 + 6 =3D 6x – = 3x
        12 =3D 3x
        = ;  4 =3D x 
Solving Rational Equations
To solve = an equation with fractional terms, we first clear the fractions= by multiplying both sides by the LCD.
Example B.  Solve
3
x – 1
=3D
6
x + 2
Multiply both sides by the LCD =3D (x – 1)(x + 2)
3
x – 1
=3D
6
x + 2
(
) *
(x – 1)(x + 2)
(x – 1) =
(x + 2)
Note that in this proportional equation, multiplying the LCD
yield the same equation if we cross-multiplied= .
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0093_image093.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAp AAEAgAAAAAAAAAIFjI+py1kAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0093_image094.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAo AAEAgAAAAAAAAAIFjI+py1gAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0093_image095.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAp AAEAgAAAAAAAAAIFjI+py1kAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0093_image096.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAp AAEAgAAAAAAAAAIFjI+py1kAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0093_image097.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAt AAoAgAAAAAAAAAIghI+pyxvRomSvzhvrw1xp2IXAJ4ZkyZ3opa5S675bLBYAOx== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0093_image098.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhXwAQAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQBe AA4AgAAAAAAAAAI5hI+py+0PYZgh2oszo1z7DxocFZbmM07nyoppC4epGtfZbOcXrvcO7wsmgMIi sRg8InvKJbPjjB4KADs= ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0093_image099.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAs AAoAgAAAAAAAAAIghI+pyxsNIwuUytuqxRzp14VfKGpkN55Yqkps625wWAAAOw== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0069.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
Example C.  Solve
2
x – 2
=3D
4
x + 1
+ 1
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0094.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
Example C.  Solve
2
x – 2
=3D
4
x + 1
Multiply both sides by the LCD : (x – 2)(x + 1)
+ 1
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0094_image100.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAo AAEAgAAAAAAAAAIFjI+py1gAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0094_image101.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAo AAEAgAAAAAAAAAIFjI+py1gAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0095.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
Example C.  Solve
2
x – 2
=3D
4
x + 1
Multiply both sides by the LCD : (x – 2)(x + 1)
2
x – 2
=3D
4
x + 1
(
) *
(x – 2)(x + 1)
+ 1
+ 1
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0095_image102.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAo AAEAgAAAAAAAAAIFjI+py1gAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0095_image103.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAo AAEAgAAAAAAAAAIFjI+py1gAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0095_image104.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAo AAEAgAAAAAAAAAIFjI+py1gAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0095_image105.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAp AAEAgAAAAAAAAAIFjI+py1kAO1== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0070.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
Example C.  Solve
2
x – 2
=3D
4
x + 1
Multiply both sides by the LCD : (x – 2)(x + 1)
2
x – 2
=3D
4
x + 1
(
) *
(x – 2)(x + 1)
+ 1
+ 1
(x + 1)
------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0070_image106.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhLwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAt AAoAgAAAAAAAAAIghI+pyxvRomSvzhvrw1xp2IXAJ4ZkyZ3opa5S675bLBYAOx== ------=_NextPart_01C95E52.E3A85980 Content-Location: file:///C:/09764A33/9SolvingRationalEquations_files/slide0096.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
Example C.  Solve
2
x – 2
=3D
4
x + 1
Multiply both sides by the LCD : (x – 2)(x + 1)
2
x – 2
=3D
4
x + 1