Rewrite each rational expression with the indicated denominator. See Examples 4 and 5.

51. 
    
    
    
    52. 
        
        
        
        53. 
            
        
        
        
        
    
    
    
    


52. 
    
    
    
    55. 
        
        
        
        56. 
            
        
        
        
        
    
    
    
    


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    58. 
        
    
    
    
    


54. 
    
    
    
    60. 
        
    
    
    
    


55. 
    
    
    
    62. 
        
    
    
    
    

63.

64.

65.

66.

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68. 
    
    
    
    70. 
        
    
    
    
    

2 p+ 3 q

p^2 + 2 pq+q^2

=

?

1 p+q 21 p^3 +q^32

21 z-y 2

y^2 +yz+z^2

=

?

y^4 - z^3 y

3 x- 1

x^2 + 2 x+ 4

=

?

x^3 - 8

4 r-t

r^2 +rt+t^2

=

?

t^3 - r^3

m- 4

6 m^2 + 7 m- 3

=

?

12 m^3 + 14 m^2 - 6 m

a+ 2 b

2 a^2 +ab-b^2

=

?

2 a^3 b+a^2 b^2 - ab^3

4 m

m^2 +m- 2

=

?

1 m- 121 m- 321 m+ 22

36 r

r^2 - r- 6

=

?

1 r- 321 r+ 221 r+ 12

25

m^2 - 9 m

=

?

m 1 m- 921 m+ 82

6

k^2 - 4 k

=

?

k 1 k- 421 k+ 12

• 
  

  7 y
  6 y+ 18

  
  

?

24 y+ 72

• 
  

  2 a
  9 a- 18

  
  

?

18 a- 36

3 r

5 r- 5

=

?

15 r- 15

19 z

2 z- 6

=

?

6 z- 18

7 t^2

3 y

=

?

9 y^2

15 m^2

8 k

=

?

32 k^4

• 4
  q

=

?

6 q

• 5
  k

=

?

9 k

8

7

=

?

42

4

11

=

?

55

440 CHAPTER 7 Rational Expressions and Applications

Add or subtract as indicated. Write each answer in lowest terms. See Section 1.1.

71. 
    
    
    
    72. 
        
        
        
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            74. 
                
            
            
            
            
        
        
        
        
    
    
    
    

11

6

• 
  

2

5

7

5

• 
  

3

4

2

3

+

8

27

1

2

+

7

8

PREVIEW EXERCISES

OBJECTIVES OBJECTIVE 1 Add rational expressions having the same denominator.

We find the sum of two rational expressions with the same denominator using the

same procedure that we used in Section 1.1for adding two common fractions.

Adding and Subtracting Rational Expressions

7.4

1 Add rational

expressions having

the same

denominator.

2 Add rational

expressions having

different

denominators.

3 Subtract rational

expressions.

Adding Rational Expressions (Same Denominator)

The rational expressions and are added as follows.

That is, to add rational expressions with the same denominator, add the numera-

tors and keep the same denominator.

P

Q



R

Q



PR

Q

QP QR^1 QZ^02

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