NAME
DATE
11-4
PERIOD
Study Guide and Intervention
Multiplying and Dividing Rational Expressions
Multiply Rational Expressions
To multiply rational expressions, you multiply the
numerators and multiply the denominators. Then simplify.
2
2c f a 2b
.
Find −2 · −
Example 1
3cf
5ab
2c 2f a 2b
2a 2bc 2f
−2 · −
= −
2
3cf
5ab
Multiply.
15ab cf
1
(abcf)(2ac)
(abcf)(15b)
= −
1
Simplify.
2ac
= −
Simplify.
15b
x+4
x 2 - 16
Find −
· −
.
2
Example 2
2x + 8
2
x + 8x + 16
(x - 4)(x + 4)
2(x + 4)
x+4
x + 8x + 16
x+4
(x + 4)(x + 4)
x - 16
−
· −
= − · −
2
2x + 8
1
(x - 4)(x + 4)
2(x + 4)1
1
x+4
(x + 4)(x + 4)1
= −·−
Simplify.
x-4
=−
Multiply.
2x + 8
Exercises
Find each product.
ab
b
4
2. − · −
mp −
b
x+2
x-1
x+2 x-4
3. − · −
x-4
x-1
n-4
8
2x + 2
2x + 16
4
x-1
x - 3x + 2
2
a 2 + 7a + 12
a + 2a - 8
a-5
2x + 16
(a + 5)(a - 2)
x+2
x-2
m -1
−2
10. −
· −
2
2
n-1
n-2
12. − · −
2
2
2
n + 6n + 5
a 2 + 3a - 10
a + 2a - 8
a+2
−
n -1
n - 25
·−
11. −
2
2
n - 7n + 10
x + 16x + 64
a 2 - 25
a2 - 4
8. −
· −
−
x 2 + 6x + 8
x2 - x - 1
9. −
· 2−
2
2
2x + 9x + 4
m-5
x-8
x+8
x 2 - 64
−
6. −
· −
2
4
8x + 8
x-1
·−
7. −
2
x - 2x + 1
m-5
16
4. −
·−
2
−
2n - 8 2n + 4
5. −
·−
n+2
4p
3
mp 2
3
6ab a 2 6a
· −2 −
1. −
2 2
3
13. −
· −
2
2
−
2
3p - 3r
10pr
m+1
(m - 1)
2m + 1
m - 2m + 1
2m - m - 1
20p 2r 2
p-r
6pr
p+r
−
2
v 2 + 8v
- 4v - 21
14. v−
· −
2
2
3v + 6v
v + 11v + 24
v-7
−
3v + 6
(a + 3)(a + 5)
−
(a - 2)(a + 4)
Chapter 11
23
Glencoe Algebra 1
Lesson 11-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Factor.
NAME
DATE
11-4
PERIOD
Study Guide and Intervention
(continued)
Multiplying and Dividing Rational Expressions
Divide Rational Expressions
To divide rational expressions, multiply by the
reciprocal of the divisor. Then simplify.
12c 2f
5a b
Example 1
2
c 2f 2
10ab
÷ −.
Find −
2 2
2 2
2
12c f
cf
12c f
10ab
−
÷−=−
×−
2 2
2 2
2 2
10ab
5a b
5a b
1 2 1
12 c f
cf
2
10 1ab 1
× −
=−
2 2
2 2
5ab
24
=−
abf
1 a
cf
1
b
f
x 2 + 6x - 27
x + 11x + 18
Example 2
x-3
÷ −
.
Find −
2
2
x 2 + 6x - 27
x + 11x + 18
x +x-2
x 2 + 6x - 27
x + 11x + 18
x2 + x - 2
x-3
(x + 9)(x - 3)
(x + 9)(x + 2)
(x + 2)(x - 1)
x-3
x-3
−
÷−
= −
× −
2
2
2
x +x-2
= − × −
1
1
(x + 9)(x - 3)
(x + 9)(x + 2)1
1
1
(x + 2)(x - 1)
x - 31
= − × −
Exercises
Find each quotient.
p
12ab
b 12
÷−
1. −
a −
a 2b 2
b2
n
n
2. −
÷−
p −
4
4
y
16
3xy 2
8
3. − ÷ 6xy −
m-5
m-5
4. −
÷−
2
1
2n - 4
n2 - 4
−
5. −
÷−
n
2n
n+2
6. −
÷− −
2
x 2 - 5x + 6
x-3
7. − ÷ −
3(x - 2)
2
a 2b 3c
6a 2bc 4b tu
−
8. −
÷−
2
2
5
x 2 + 6x + 8
x + 4x + 4
8
y 2 - 36
y - 49
15
y+6 y-6
y+7 y-7
8rt u
9r
m 2 - 13m + 42 3m(m + 7)
m 2 - 49
−
10. −
÷ −
m
3m 2
m-6
x+4
x+2
9. −
÷ − 1
2
n 2 - 5n + 6
n + 3n
3r t
16
-4(n - 2)
p 2 - 2pr + r 2
p2 - r2 p - r
−
−
12. −
÷
p+r
p+r p+r
n
(a + 4)(a - 5)
a + 3 (a - 3)(2a + 1)
a2 - 9
− 14. −
−
÷ −
2
2a + 13a - 7
4a 2 - 1
a+7
(a - 2)(a - 3)
3-n
−
11. −
÷ −
2
4n + 12
a 2 + 7a + 12
a2 - 9
13. −
÷ −
2
2
a + 3a - 10
Chapter 11
a - 25
24
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
=x-1