Name
11-2
Class
Date
Practice
Form G
Multiplying and Dividing Rational Expressions
Multiply.
22z 3
1. 4 1 5z ? z
x29
x
2. x 1 7 ? x 2 6
6 2 3z
4z 1 5z2
x2 2 9x
x2 1 x 2 42
3.
5w 2 25
w
?
5w2 2 10 w2 2 25
4.
w
w2 1 3w 2 10
5.
3u3 2 6u2
7u 2 3
39j
j2 1 11j 2 42
?j23
26j 2 52
6.
15r
3r 2 3
?
18r2 1 9r 2 27
r2
5
2r2 1 3r
3j2 1 42j
2j 2 4
7.
16u 2 32
3u3
? 56u 2 24
2u
45q2 2 3q 2 6
14q2 1 10q
?
2
q
35q2 1 11q 2 10
4y 1 17
8. 2y 2 3 ? (32y2 2 22y 2 39)
64y2 1 324y 1 221
18q 1 6
q
9. (12v2 1 18v 2 84) ?
4v3
v
2 49v
10. (10x2 2 7x 1 2) ?
6v 2 12
2v 2 7
6x2 2 13x 2 63
3x 1 7
20x3 2 104x2 1 67x 2 18
11. Which of the following is the reciprocal of x2 2 2x 2 8? B
1
A. (x 1 2)(x 2 4)
B.
(x 1 2)(x 2 4)
1
C. x 2 8
Find the reciprocal of each expression.
12. x2 2 4x 1 18
13.
1
x2 2 4x 1 18
3q2
2q2 2 13
2q2 2 13
3q2
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Name
Class
11-2
Date
Practice (continued)
Form G
Multiplying and Dividing Rational Expressions
Divide.
5y 1 7
5y 1 7
14. 3y 1 19 4 y 2 6
15.
y26
3y 1 19
25i2 2 36
5i 2 6
4 8i
56i
5i 1 6
7
12j 2 36
3j 2 9
16. 2j 1 4 4 2
4j 2 16
17.
8j 2 16
12x2 1 x 2 13
x21
4 2
45x2 2 20x 2 25
9x 1 5
12x 1 13
5x 2 5
18. (72k2 1 29k 2 21) 4
9k2 2 92k 2 77
6k 2 1
(8k 2 3)(6k 2 1)
k 2 11
Simplify each complex fraction.
19.
a
11
b
20. x
13
b
111
x
9
18
x
21.
a 1 b
x 1 3b
1
b
a1a
1
b
b 1 b2
a
22. A rectangular prism has a base area of 3x2 1 21x 2 24 and a height of
x
33x 2 33 . What is the volume of the prism?
x(x 1 8)
11
units3
1
23. Your friend runs for (x2 2 225) seconds at a rate of 2x 2 30 meters per
second. How far does your friend run?
x 1 15
2
meters
24. Writing How do you simplify a complex fraction?
Answers may vary. Sample: Multiply the numerator by the reciprocal of the
denominator. Then factor out as many like terms as possible to simplify.
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Name
11-2
Class
Date
Practice
Form K
Multiplying and Dividing Rational Expressions
Multiply.
1.
5n2 3 5
?
n
3n2 n
t(t 1 1)
t
t11
2. t 2 3 ? t 1 2 (t 2 3)(t 1 2)
3a 2 9
a
a
3. 3a 2 6 ? 2
a 2 9 (a 1 3)(a 2 2)
5.
m2 2 m 2 20
2m2
? 2
2
m 2 4m
m 2 25
4.
18q 2 36
4q2
2q(q 2 2)
?
2q
54q 2 18 (3q 2 1)
6.
8v
3v 2 1
?
6v2 1 22v 2 8
4v2
1
v(v 1 4)
2m(m 1 4)
(m 2 4)(m 1 5)
2z2 2 7z 1 5
z2
7. 2
?
z 1 5z 2 6
6z2 2 15z
8. (3x2 1 7x 1 4) ?
z
3(z 1 6)
x2 2 4x
9x3 2 16x
(x 1 1)(x 2 4)
3x 2 4
9. Which of the following is the reciprocal of x2 2 2x 2 63? a
1
1
a.
b. (x 1 7)(x 2 9)
c. x 2 9
(x 1 7)(x 2 9)
Find the reciprocal of each expression.
1
10. x2 2 2x 2 15 (x 2 5)(x 1 3)
11.
6p2
7p2 2 12
2
6p2
7p 2 12
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15
Name
Class
11-2
Date
Practice (continued)
Form K
Multiplying and Dividing Rational Expressions
Divide.
12.
6f 2 6
6f 2 6 f 1 9
4 f 1 9 3f
28
3f 2 8
13.
12m 2 20
3m 2 5 4
4 9m
3
27m
14.
18c 2 27
2c 2 3
9
4 3t 1 4 3t 2 4
9t2 2 16
15.
2x2 2 23x 1 56
x 2 8 2x 2 7
4 5x 1 3
2
10x 1 6
Simplify each complex fraction.
1
x23
16.
3
x23
m
n 12
1
3
17. m
n 15
m 1 2n
m 1 5n
x
18. A shipping box has a base area of 4x2 1 52x 1 168 and a height of 4x 1 28 .
What is the volume of the box?
x(x 1 6)
1
19. Karl drives for (x2 2 100) hours at a rate of 5x 2 50 miles per hour. How far
does Karl drive?
x 1 10
5
miles
20. Open-Ended Write two rational expressions whose product is 1.
x 1 3
1
Answers may vary. Sample: x 1
1
3 and
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