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------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/master30.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/preview.wmf Content-Transfer-Encoding: base64 Content-Type: image/x-wmf AQAJAAAD+AAAAAUATwAAAAAABAAAAAMBCAAFAAAACwIAAAAABQAAAAwC7wLpAwMAAAAeAAcAAAD8 AgAA////AAAABAAAAC0BAAAIAAAA+gIFAAAAAAD///8ABAAAAC0BAQAMAAAAQAkhAPAAAAAAAAAA 7wLpA/////8IAAAA+gIAAAAAAAAAAAAABAAAAC0BAgAEAAAALQEAAAQAAAAnAf//HAAAAPsC2f8A AAAAAAC8AgAAAAAAQAAAQXJpYWwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAEAAAALQEDAAQA AAAuARgABAAAAAIBAQAFAAAACQIAAAACTwAAADIKNQA0ADAAAABBZGRpdGlvbiBhbmQgU3VidHJh Y3Rpb24gb2YgUmF0aW9uYWwgRXhwcmVzc2lvbnMbABgAGAALAA0ACwAYABgACwAWABgAGAAKABoA GAAYAA0ADwAWABYADAALABgAGAAKABgADQALABwAFgANAAsAFwAYABYACwALABkAFgAYAA8AFgAV ABYACwAYABcAFQAEAAAALgEAABwAAAD7AhAABwAAAAAAvAIAAAAAAQICIlN5c3RlbQAAAAAAABgA AAAsnhMAAQAAAOQEAAAAAAAABAAAAC0BBAAEAAAA8AEDAAMAAAAAAA== ------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0002.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Addition and Subtraction of Rational Expressions
Only fractions with the same denominator may be added or subtracted directly.
------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0097.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Addition and Subtraction of Rational Expressions
Additi= on and Subtraction Rule
(for rati= onal expressions with the same denominator)
Only fractions with th= e same denominator may be added or subtracted directly.
A
B
D
D
&plu= smn;
=3D
A&plu= smn;B<= /div>
D
------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0098.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Addition and Subtraction of Rational Expressions
Additi= on and Subtraction Rule
(for rati= onal expressions with the same denominator)
Only fractions with th= e same denominator may be added or subtracted directly.
A
B
D
D
&plu= smn;
=3D
A&plu= smn;B<= /div>
D
Usually we put the res= ult in the factored form, cancel the common factor and give= the simplified answer.
------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0099.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Addition and Subtraction of Rational Expressions
Additi= on and Subtraction Rule
(for rati= onal expressions with the same denominator)
Only fractions with th= e same denominator may be added or subtracted directly.
A
B
D
D
&plu= smn;
=3D
A&plu= smn;B<= /div>
D
Usually we put the res= ult in the factored form, cancel the common factor and give= the simplified answer.
Example A. Add and subtract and simplify the answer.
a.
5
7
8
8
+
=3D<= /div>
------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0100.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Addition and Subtraction of Rational Expressions
Additi= on and Subtraction Rule
(for rati= onal expressions with the same denominator)
Only fractions with th= e same denominator may be added or subtracted directly.
A
B
D
D
&plu= smn;
=3D
A&plu= smn;B<= /div>
D
Usually we put the res= ult in the factored form, cancel the common factor and give= the simplified answer.
Example A. Add and subtract and simplify the answer.
a.
5
7
8
8
+
=3D<= /div>
5 + 7
8
------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0101.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Addition and Subtraction of Rational Expressions
Additi= on and Subtraction Rule
(for rati= onal expressions with the same denominator)
Only fractions with th= e same denominator may be added or subtracted directly.
A
B
D
D
&plu= smn;
=3D
A&plu= smn;B<= /div>
D
Usually we put the res= ult in the factored form, cancel the common factor and give= the simplified answer.
Example A. Add and subtract and simplify the answer.
a.
5
7
8
8
+
=3D<= /div>
5 + 7
8
=3D<= /div>
12
8
------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0102.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Addition and Subtraction of Rational Expressions
Additi= on and Subtraction Rule
(for rati= onal expressions with the same denominator)
Only fractions with th= e same denominator may be added or subtracted directly.
A
B
D
D
&plu= smn;
=3D
A&plu= smn;B<= /div>
D
Usually we put the res= ult in the factored form, cancel the common factor and give= the simplified answer.
Example A. Add and subtract and simplify the answer.
a.
5
7
8
8
+
=3D<= /div>
5 + 7
8
=3D<= /div>
12
8
3
2
------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0103.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Addition and Subtraction of Rational Expressions
Additi= on and Subtraction Rule
(for rati= onal expressions with the same denominator)
Only fractions with th= e same denominator may be added or subtracted directly.
A
B
D
D
&plu= smn;
=3D
A&plu= smn;B<= /div>
D
Usually we put the res= ult in the factored form, cancel the common factor and give= the simplified answer.
Example A. Add and subtract and simplify the answer.
a.
5
7
8
8
+
=3D<= /div>
5 + 7
8
=3D<= /div>
12
8
=3D<= /div>
3
2
3
2
------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0104.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Addition and Subtraction of Rational Expressions
Additi= on and Subtraction Rule
(for rati= onal expressions with the same denominator)
Only fractions with th= e same denominator may be added or subtracted directly.
A
B
D
D
&plu= smn;
=3D
A&plu= smn;B<= /div>
D
Usually we put the res= ult in the factored form, cancel the common factor and give= the simplified answer.
Example A. Add and subtract and simplify the answer.
a.
5
7
8
8
+
=3D<= /div>
5 + 7
8
=3D<= /div>
12
8
=3D<= /div>
3
2
3
2
b.
3x
2x – 3
–
6 – x
2x – 3
------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0105.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Addition and Subtraction of Rational Expressions
Additi= on and Subtraction Rule
(for rati= onal expressions with the same denominator)
Only fractions with th= e same denominator may be added or subtracted directly.
A
B
D
D
&plu= smn;
<= ![endif]>
=3D
A&plu= smn;B<= /div>
D
Usually we put the res= ult in the factored form, cancel the common factor and give= the simplified answer.
Example A. Add and subtract and simplify the answer.
a.
5
7
8
8
+ <= ![endif]>
=3D<= /div>
5 + 7
8
=3D<= /div>
12
8
=3D<= /div>
3
2
3
2
b.
3x
2x – 3
–
6 – x
2x – 3
=3D
3x – (6 – x) 
2x – 3
------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0105.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0106.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Addition and Subtraction of Rational Expressions
Additi= on and Subtraction Rule
(for rati= onal expressions with the same denominator)
Only fractions with th= e same denominator may be added or subtracted directly.
A
B
D
D
&plu= smn;
<= ![endif]>
=3D
A&plu= smn;B<= /div>
D
Usually we put the res= ult in the factored form, cancel the common factor and give= the simplified answer.
Example A. Add and subtract and simplify the answer.
a.
5
7
8
8
+ <= ![endif]>
=3D<= /div>
5 + 7
8
=3D<= /div>
12
8
=3D<= /div>
3
2
3
2
b.
3x
2x – 3
–
6 – x
2x – 3
=3D
3x – (6 – x) 
2x – 3
=3D
3x – 6 + x 
2x – 3
------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0106.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0107.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Addition and Subtraction of Rational Expressions
Additi= on and Subtraction Rule
(for rati= onal expressions with the same denominator)
Only fractions with th= e same denominator may be added or subtracted directly.
A
B
D
D
&plu= smn;
<= ![endif]>
=3D
A&plu= smn;B<= /div>
D
Usually we put the res= ult in the factored form, cancel the common factor and give= the simplified answer.
Example A. Add and subtract and simplify the answer.
a.
5
7
8
8
+ <= ![endif]>
=3D<= /div>
5 + 7
8
=3D<= /div>
12
8
=3D<= /div>
3
2
3
2
b.
3x
2x – 3
–
6 – x
2x – 3
=3D
3x – (6 – x) 
2x – 3
=3D
3x – 6 + x 
2x – 3
=3D
4x – 6  
2x – 3
------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0107.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0108.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Addition and Subtraction of Rational Expressions
Additi= on and Subtraction Rule
(for rati= onal expressions with the same denominator)
Only fractions with th= e same denominator may be added or subtracted directly.
A
B
D
D
&plu= smn;
<= ![endif]>
=3D
A&plu= smn;B<= /div>
D
Usually we put the res= ult in the factored form, cancel the common factor and give= the simplified answer.
Example A. Add and subtract and simplify the answer.
a.
5
7
8
8
+ <= ![endif]>
=3D<= /div>
5 + 7
8
=3D<= /div>
12
8
=3D<= /div>
3
2
3
2
b.
3x
2x – 3
–
6 – x
2x – 3
=3D
3x – (6 – x) 
2x – 3
=3D
3x – 6 + x 
2x – 3
=3D
4x – 6  
2x – 3
=3D
2(2x – 3)
2x – 3
------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0108.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0109.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Addition and Subtraction of Rational Expressions
Additi= on and Subtraction Rule
(for rati= onal expressions with the same denominator)
Only fractions with th= e same denominator may be added or subtracted directly.
A
B
D
D
&plu= smn;
<= ![endif]>
=3D
A&plu= smn;B<= /div>
D
Usually we put the res= ult in the factored form, cancel the common factor and give= the simplified answer.
Example A. Add and subtract and simplify the answer.
a.
5
7
8
8
+ <= ![endif]>
=3D<= /div>
5 + 7
8
=3D<= /div>
12
8
=3D<= /div>
3
2
3
2
b.
3x
2x – 3
–
6 – x
2x – 3
=3D
3x – (6 – x) 
2x – 3
=3D
3x – 6 + x 
2x – 3
=3D
4x – 6  
2x – 3
=3D
2(2x – 3)
2x – 3
------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0109.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0110.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
Addition and Subtraction of Rational Expressions
Additi= on and Subtraction Rule
(for rati= onal expressions with the same denominator)
Only fractions with th= e same denominator may be added or subtracted directly.
A
B
D
D
&plu= smn;
<= ![endif]>
=3D
A&plu= smn;B<= /div>
D
Usually we put the res= ult in the factored form, cancel the common factor and give= the simplified answer.
Example A. Add and subtract and simplify the answer.
a.
5
7
8
8
+ <= ![endif]>
=3D<= /div>
5 + 7
8
=3D<= /div>
12
8
=3D<= /div>
3
2
3
2
b.
3x
2x – 3
–
6 – x
2x – 3
=3D
3x – (6 – x) 
2x – 3
=3D
3x – 6 + x 
2x – 3
=3D
4x – 6  
2x – 3
=3D
2(2x – 3)
2x – 3
=3D 2
------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0110.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0012.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
To add or subtract rat= ional expressions with different denominators, they hav= e to be converted to a common denominator.
Addition and Subtraction of Rational Expressions
------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0111.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
To add or subtract rat= ional expressions with different denominators, they hav= e to be converted to a common denominator. The easie= st common denominator to work with is their LCM.
Addition and Subtraction of Rational Expressions
------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0112.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
To add or subtract rat= ional expressions with different denominators, they hav= e to be converted to a common denominator. The easie= st common denominator to work with is their LCM.
Addition and Subtraction of Rational Expressions
Conver= sion Theorem
Given the fraction     ,=   to convert it into denominator D,=
the new numerator is
A
B
A
B
* D.
------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0089.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
To add or subtract rat= ional expressions with different denominators, they hav= e to be converted to a common denominator. The easie= st common denominator to work with is their LCM.
Addition and Subtraction of Rational Expressions
Conver= sion Theorem
Given the fraction     ,=   to convert it into denominator D,=
the new numerator is
A
B
A
B
* D.
In practice, we write this as
A
B
=3D
A
B
* D
D
numerator
------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0113.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
To add or subtract rat= ional expressions with different denominators, they hav= e to be converted to a common denominator. The easie= st common denominator to work with is their LCM.
Addition and Subtraction of Rational Expressions
Conver= sion Theorem
Given the fraction     ,=   to convert it into denominator D,=
the new numerator is
Example B. 
a. Convert      to a fraction with denominator 12.        = ;        
A
B
A
B
* D.
5
4
In practice, we write this as
A
B
=3D
A
B
* D
D
numerator
------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0114.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
To add or subtract rat= ional expressions with different denominators, they hav= e to be converted to a common denominator. The easie= st common denominator to work with is their LCM.
Addition and Subtraction of Rational Expressions
Conver= sion Theorem
Given the fraction     ,=   to convert it into denominator D,=
the new numerator is
Example B. 
a. Convert      to a fraction with denominator 12.        = ;        
A
B
A
B
* D.
5
4
In practice, we write this as
A
B
=3D
A
B
* D
D
numerator
5
4
=3D
------=_NextPart_01C95D3B.841BD540 Content-Location: file:///C:/486BB24E/6AdditionandSubtraction_files/slide0115.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Addition and Subtraction
To add or subtract rat= ional expressions with different denominators, they hav= e to be converted to a common denominator. The easie= st common denominator to work with is their LCM.
Addition and Subtraction of Rational Expressions
Conver= sion Theorem
Given the fraction     ,=   to convert it into denominator D,=
the new numerator is
Example B. 
a. Convert      to a fraction with denominator 12.        = ;        
A
B
A
B
* D.
5
4
5
4
* 12 
In practice, we write this as
A
B
=3D
A
B
* D
D