Dividing Rational Expressions

Divide.

(a)

Multiply by the

reciprocal.

Factor.

Multiply; lowest

terms

=

4

5 z

=

2 z

9

#^2

# 9

5 z#z

=

2 z

9

#^18

5 z^2

2 z

9

,

5 z^2

18

EXAMPLE 5

368 CHAPTER 7 Rational Expressions and Functions

(b)

Multiply by

the reciprocal.

Properties of

exponents

Properties of

exponents

=

q^4

m^3 p^4

=

m^3 p^2 q^5

m^6 p^6 q

=

m^2 pq^3

mp^4

mpq

2

m^5 p^2 q

m^2 pq^3

mp^4

,

m^5 p^2 q

mpq^2

(c)

Multiply by the reciprocal.

Factor.

Multiply; lowest terms

(d)

Definition of division

Factor.

Lowest terms

NOW TRY

=

5 m- 3

m+ 1

=

15 m- 321 m+ 42

1 m+ 4213 m- 52

13 m- 5215 m- 32

15 m- 321 m+ 12

=

5 m^2 + 17 m- 12

3 m^2 + 7 m- 20

#^15 m

(^2) - 34 m+ 15

5 m^2 + 2 m- 3

5 m^2 + 17 m- 12

3 m^2 + 7 m- 20

,

5 m^2 + 2 m- 3

15 m^2 - 34 m+ 15

=

32 k

9

=

81 k- 22

3 k

#^4 k

#k

31 k- 22

=

8 k- 16

3 k

#^4 k

2

3 k- 6

8 k- 16

3 k

,

3 k- 6

4 k^2

NOW TRY
EXERCISE 5
Divide.

(a)

(b)

3 k^2 + 5 k- 2

9 k^2 - 1

,

4 k^2 + 8 k

k^2 - 7 k

2 p^2 q

3 pq^4

,

pq

6 p^2 q^2

NOW TRY ANSWERS

5. (a) (b)
   k- 7
   413 k+ 12

4 p^2

q^2

Complete solution available
on the Video Resources on DVD

7.1 EXERCISES

For each rational function, find all numbers that are not in the domain. Then give the domain,

using set-builder notation. See Example 1.

1. 
   
   
   
   2. 
      
      
      
      3. 
         
      
      
      
      
   
   
   
   

4. 5. 6.

7. 8. 9.

10. 
    
    
    
    11. 12.ƒ 1 x 2 =
    
    
    
    

9 x^2 - 8 x+ 3

4 x^2 + 1

ƒ 1 x 2 =

2 x^2 - 3 x+ 4

3 x^2 + 8

ƒ 1 x 2 =

x- 9

26

ƒ 1 x 2 =

x+ 2

14

ƒ 1 x 2 =

2 x+ 4

3 x^2 + 11 x- 42

ƒ 1 x 2 =

3 x+ 1

2 x^2 +x- 6

ƒ 1 x 2 =

9 x+ 8

x

ƒ 1 x 2 =

12 x+ 3

x

ƒ 1 x 2 =

8 x- 3

2 x+ 7

ƒ 1 x 2 =

6 x- 5

7 x+ 1

ƒ 1 x 2 =

x

x+ 3

ƒ 1 x 2 =

x

x- 7