Beginning Algebra, 11th Edition

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    55. 
        
        
        
        56. 
            
        
        
        
        
    
    
    
    


55. 
    
    
    
    58. 
        
    
    
    
    


56. 
    
    
    
    60. 
        
    
    
    
    

In these subtraction problems, the rational expression that follows the subtraction sign has a
numerator with more than one term. Be careful with signsand find each difference. See
Example 9.

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    62. 
        
    
    
    
    


62. 
    
    
    
    64. 
        
    
    
    
    


63. 
    
    
    
    66. 
        
    
    
    
    

Perform each indicated operation. See Examples 1–9.

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    68. 
        
    
    
    
    


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    70. 
        
    
    
    
    


69. 
    
    
    
    72. 
        
    
    
    
    

2 x-z

2 x^2 +xz- 10 z^2

• 
  

x+z

x^2 - 4 z^2

r+y

18 r^2 + 9 ry- 2 y^2

+

3 r-y

36 r^2 - y^2

m

m^2 - 1

+

m- 1

m^2 + 2 m+ 1

x+ 3 y

x^2 + 2 xy+y^2

+

x-y

x^2 + 4 xy+ 3 y^2

6

k^2 + 3 k

• 
  

1

k^2 - k

+

2

k^2 + 2 k- 3

4

r^2 - r

+

6

r^2 + 2 r

• 
  

1

r^2 +r- 2

4 y- 1

2 y^2 + 5 y- 3

• 
  

y+ 3

6 y^2 +y- 2

2 q+ 1

3 q^2 + 10 q- 8

• 
  

3 q+ 5

2 q^2 + 5 q- 12

1

a^2 - 1

• 
  

a- 1

a^2 + 3 a- 4

5

x^2 - 9

• 
  

x+ 2

x^2 + 4 x+ 3

5 p

p-q

• 
  

3 p+ 1

4 p- 4 q

2 m

m-n

• 5 m+n
  2 m- 2 n

8

3 - 7 y

• 2
  7 y- 3

3

4 p- 5

+

9

5 - 4 p

t

8 t- 9 s

• 
  

s

9 s- 8 t

x

5 x- 3 y

• 
  

y

3 y- 5 x

• 8
  p-q^2

• 
  

3

q^2 - p

2

x-y^2

+

7

y^2 - x

• 4
  p- 3


• 
  

p+ 1

3 - p

SECTION 7.4 Adding and Subtracting Rational Expressions 447

73.Refer to the rectangle in the figure.

(a)Find an expression that represents its

perimeter. Give the simplified form.

(b)Find an expression that represents its

area. Give the simplified form.

74.Refer to the triangle in the figure. Find an

expression that represents its perimeter.

5

6 k + 2

3 k + 1

10

9

2 p

1

p^2

3

p^2

A concours d’eleganceis a competition in which a
maximum of 100 points is awarded to a car based on
its general attractiveness. The rational expression

approximates the cost, in thousands of dollars, of
restoring a car so that it will win x points.
Use this information to work Exercises 75 and 76.

75.Simplify the given expression by performing the
indicated subtraction.

76.Use the simplified expression from Exercise 75to determine how much it would cost to
win 95 points.

1010

491101 - x 2

• 10
  49