SECTION 7.2 Multiplying and Dividing Rational Expressions 433

Complete solution available
on the Video Resources on DVD

1.Concept Check Match each multipli-

cation problem in Column I with the

correct product in Column II.

III

(a) A.

(b) B.

(c) C.

(d) D.

2.Concept Check Match each division

problem in Column I with the correct

quotient in Column II.

III

(a) A.

(b) B.

(c) C.

(d) D.

1

5 x^7

10 x^4

5 x^3

,

4 x

10 x^7

4

5 x^5

5 x^3

10 x^4

,

4 x

10 x^7

5 x^7

10 x^4

5 x^3

,

10 x^7

4 x

5 x^5

4

5 x^3

10 x^4

,

10 x^7

4 x

5 x^7

10 x^4

5 x^3

#^4 x

10 x^7

1

5 x^7

5 x^3

10 x^4

#^4 x

10 x^7

5 x^5

4

10 x^4

5 x^3

#^10 x

7

4 x

4

5 x^5

5 x^3

10 x^4

#^10 x

7

4 x

7.2 EXERCISES

Multiply. Write each answer in lowest terms. See Examples 1 and 2.

3. 
   
   
   
   4. 
      
      
      
      5. 
         
      
      
      
      
   
   
   
   


4. 
   
   
   
   7. 
      
      
      
      8. 
         
      
      
      
      
   
   
   
   


5. 
   
   
   
   10. 
       
       
       
       11. 
           
       
       
       
       
   
   
   
   


6. 
   
   
   
   13. 
       
       
       
       14. 
           
       
       
       
       
   
   
   
   

Divide. Write each answer in lowest terms. See Examples 4 and 5.

15. 
    
    
    
    16. 
        
        
        
        17. 
            
        
        
        
        
    
    
    
    


16. 
    
    
    
    19. 
        
        
        
        20. 
            
        
        
        
        
    
    
    
    


17. 
    
    
    
    22. 
        
        
        
        23. 
            
        
        
        
        
    
    
    
    


18. 
    
    
    
    25. 
        
        
        
        26. 
            
        
        
        
        
    
    
    
    

Multiply or divide. Write each answer in lowest terms. See Examples 3, 6, and 7.

27. 
    
    
    
    28. 
        
        
        
        29. 
            
        
        
        
        
    
    
    
    


28. 
    
    
    
    31. 
        
        
        
        32. 
            
        
        
        
        
    
    
    
    


29. 
    
    
    
    34. 
        
        
        
        35. 
            
        
        
        
        
    
    
    
    


30. 
    
    
    
    37. 
        
        
        
        38. 
            
        
        
        
        
    
    
    
    


31. 
    
    
    
    40. 3 t^2 - 4 t- 4
        3 t^2 + 10 t+ 8
    
    
    
    

,

9 t^2 + 21 t+ 10

3 t^2 + 14 t+ 15

2 k^2 - k- 1

2 k^2 + 5 k+ 3

,

4 k^2 - 1

2 k^2 +k- 3

3 x^2 - 5 x- 2

x- 2

# x-^3

x+ 1

2 x^2 - 7 x+ 3

x- 3

#x+^2

x- 1

r^2 - 36

54 - 9 r

,

r+ 6

9

m^2 - 4

16 - 8 m

,

m+ 2

8

z^2 - 3 z+ 2

z^2 + 4 z+ 3

,

z- 1

z+ 1

p^2 + 4 p- 5

p^2 + 7 p+ 10

,

p- 1

p+ 4

35 - 5 x

6

#^12

3 x- 21

27 - 3 z

4

#^12

2 z- 18

m- 2

4

,

2 - m

6

2 - t

8

,

t- 2

6

8 r+ 16

24 r- 24

#^6 r-^6

3 r+ 6

5 x- 15

3 x+ 9

#^4 x+^12

6 x- 18

2 a

a+ 4

,

a^2

1 a+ 422

1 x- 322

6 x

,

x- 3

x^2

y^2

y+ 1

,

3 y

y- 3

2 x

x- 1

,

x^2

x+ 2

8 z- 16

• 20

,

3 z- 6

40

7 t+ 7

• 6

,

4 t+ 4

15

4 m+ 16

10

,

3 m+ 12

18

3

2 y- 6

,

6

y- 3

• 12 a^6
  3 a^2

,

12 a 23

27 a

4 t^4

2 t^5

,

12 t 23

• 6

35 x^8

7 x^9

,

5 x^5

9 x^6

9 z^4

3 z^5

,

3 z^2

5 z^3

1 t- 222

4 t^2

#^2 t

t- 2

3 x

x+ 3

#

1 x+ 322

6 x^2

z+ 9

12

#^3 z

2

z+ 9

t- 4

8

#^4 t

2

t- 4

1 a+b 22

5

#^30

21 a+b 2

1 x-y 22

2

#^24

31 x-y 2

41 y- 22

x

#^3 x

61 y- 222

21 c+d 2

3

#^18

61 c+d 22

12 m^5

• 2 m^2

#^6 m

6

28 m^3

12 x^4

18 x^3

-^8 x

5

4 x^2

21 b^6

18

#^9

7 b^4

15 a^2

14

#^7

5 a