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Solving Rational Equations
------=_NextPart_01C99CA9.89817AA0 Content-Location: file:///C:/09764A33/2SolvingRationalEquations_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_01C99CA9.89817AA0 Content-Location: file:///C:/09764A33/2SolvingRationalEquations_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_01C99CA9.89817AA0 Content-Location: file:///C:/09764A33/2SolvingRationalEquations_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_01C99CA9.89817AA0 Content-Location: file:///C:/09764A33/2SolvingRationalEquations_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_01C99CA9.89817AA0 Content-Location: file:///C:/09764A33/2SolvingRationalEquations_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_01C99CA9.89817AA0 Content-Location: file:///C:/09764A33/2SolvingRationalEquations_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_01C99CA9.89817AA0 Content-Location: file:///C:/09764A33/2SolvingRationalEquations_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 <= /div>
Let A = =3D apple, B =3D banana, and C =3D cantaloupe
The rela= tion is
------=_NextPart_01C99CA9.89817AA0 Content-Location: file:///C:/09764A33/2SolvingRationalEquations_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 <= /div>
Distribute it to each term.
Let A = =3D apple, B =3D banana, and C =3D cantaloupe
The rela= tion is
------=_NextPart_01C99CA9.89817AA0 Content-Location: file:///C:/09764A33/2SolvingRationalEquations_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 <= /div>
Distribute it to each term.
3
Let A = =3D apple, B =3D banana, and C =3D cantaloupe
The rela= tion is
------=_NextPart_01C99CA9.89817AA0 Content-Location: file:///C:/09764A33/2SolvingRationalEquations_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 <= /div>
Distribute it to each term.
3
6
4
Let A = =3D apple, B =3D banana, and C =3D cantaloupe
The rela= tion is
------=_NextPart_01C99CA9.89817AA0 Content-Location: file:///C:/09764A33/2SolvingRationalEquations_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 <= /div>
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
------=_NextPart_01C99CA9.89817AA0 Content-Location: file:///C:/09764A33/2SolvingRationalEquations_files/slide0084.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 <= /div>
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_01C99CA9.89817AA0 Content-Location: file:///C:/09764A33/2SolvingRationalEquations_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_01C99CA9.89817AA0 Content-Location: file:///C:/09764A33/2SolvingRationalEquations_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_01C99CA9.89817AA0 Content-Location: file:///C:/09764A33/2SolvingRationalEquations_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_01C99CA9.89817AA0 Content-Location: file:///C:/09764A33/2SolvingRationalEquations_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_01C99CA9.89817AA0 Content-Location: file:///C:/09764A33/2SolvingRationalEquations_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_01C99CA9.89817AA0 Content-Location: file:///C:/09764A33/2SolvingRationalEquations_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)
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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_01C99CA9.89817AA0 Content-Location: file:///C:/09764A33/2SolvingRationalEquations_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)
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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)
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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= .
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Solving Rational Equations
Example C.  Solve
2
x – 2
=3D
4
x + 1
+ 1
------=_NextPart_01C99CA9.89817AA0 Content-Location: file:///C:/09764A33/2SolvingRationalEquations_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
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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
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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)
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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 – 2) =
(x + 1)
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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 – 2) =
(x + 1)
(x – 2)(= x + 1)
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2(x + 1) =3D 4(x – 2) + (x – 2)(x + 1)
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)