Beginning Algebra, 11th Edition

488 CHAPTER 7 Rational Expressions and Applications

7.2 Multiply or divide, and write each answer in lowest terms.

13. 
    
    
    
    14. 
        
    
    
    
    


14. 
    
    
    
    16. 
        
    
    
    
    


15. 
    
    
    
    18. 
        
    
    
    
    


16. 
    
    
    
    20. 
        
    
    
    
    

7.3 Find the least common denominator for the fractions in each list.

21. 
    
    
    
    22. 
        
    
    
    
    

Rewrite each rational expression with the given denominator.

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    24. 
        
    
    
    
    

9

x- 3

=

?

18 - 6 x

3

2 a^3

=

?

10 a^4

5

x^2 + 5 x+ 4

3

x^2 + 4 x+ 3

,

5

27 y^4

7

12 y^2

,

4

9 y

,

3 z^2 + 5 z- 2

9 z^2 - 1

#^9 z

(^2) + 6 z+ 1
z^2 + 5 z+ 6
2 p^2 + 13 p+ 20
p^2 +p- 12
#p
(^2) + 2 p- 15
2 p^2 + 7 p+ 5
y^2 - 6 y+ 8
y^2 + 3 y- 18
,
y- 4
y+ 6
6 a^2 + 7 a- 3
2 a^2 - a- 6
,
a+ 5
a- 2
2 r+ 3
r- 4
#r
(^2) - 16
6 r+ 9
x- 3
4
#^5
2 x- 6
8 x^2
12 x^5
#^6 x
4
2 x
18 p^3
6
#^24
p^4
488 CHAPTER 7 Rational Expressions and Applications

25. 
    
    
    
    26. 4 b
        b^2 + 2 b- 3
    
    
    
    

=

?

1 b+ 321 b- 121 b+ 22

• 3 y
  2 y- 10

=

?

50 - 10 y

7.4 Add or subtract, and write each answer in lowest terms.

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    28. 
        
        
        
        29. 
            
        
        
        
        
    
    
    
    


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    31. 
        
        
        
        32. 
            
        
        
        
        
    
    
    
    


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    34. 
        
    
    
    
    


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    36. 
        
    
    
    
    

7.5 Simplify each complex fraction.

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        39. 
            
        
        
        
        
    
    
    
    


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    41. 
        
        
        
        42. 
            
        
        
        
        
    
    
    
    

7.6 Solve each equation, and check your solutions.

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    44. 
        
    
    
    
    


44. 
    
    
    
    46. 
        
    
    
    
    

Solve each formula for the specified variable.

47. for t 48. for y 49.p^2 = for m

4

3 m-q

x=

3 y- 5

4

m=

Ry

t

3

m- 2

+

1

m- 1

=

7

m^2 - 3 m+ 2

3

x+ 4

• 
  

2 x

5

=

3

x+ 4

4 - z

z

+

3

2

=

• 4
  z

3 x- 1

x- 2

=

5

x- 2

+ 1

1

r+t

• 1
  1
  r+t

• 1

x^2 - 25

x+ 3

x+ 5

x^2 - 9

1

p

• 1
  q
  1
  q-p

x+

1

w

x-

1

w

2

3

• 1
  6
  1
  4

• 2
  5

y- 3

y

y+ 3

4 y

11

2 p-p^2

• 
  

2

p^2 - 5 p+ 6

8

z^2 + 6 z

• 
  

3

z^2 + 4 z- 12

4

k^2 - 9

• 
  

k+ 3

3 k- 9

5

a- 2 b

+

2

a+ 2 b

12

x^2

• 3
  4 x

m

3

• 2 + 5 m
  6

4

y

+

7

7 +y

9

k

• 
  

5

k- 5

6

3 p

• 
  

12

3 p

10

x

+

5

x

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