Beginning Algebra, 11th Edition

Note: When adding and subtracting rational expressions, several different equivalent forms of

the answer often exist. If your answer does not look exactly like the one given in the back of

the book, check to see whether you have written an equivalent form.

Add or subtract. Write each answer in lowest terms. See Examples 1 and 6.

9. 
   
   
   
   10. 
       
       
       
       11. 
           
       
       
       
       
   
   
   
   


10. 
    
    
    
    13. 
        
        
        
        14. 
            
        
        
        
        
    
    
    
    


11. 
    
    
    
    16. 
        
        
        
        17. 
            
        
        
        
        
    
    
    
    


12. 
    
    
    
    19. 
        
        
        
        20. 
            
        
        
        
        
    
    
    
    


13. 
    
    
    
    22. 
        
    
    
    
    


14. 
    
    
    
    24. 
        
    
    
    
    

Add or subtract. Write each answer in lowest terms. See Examples 2, 3, 4, and 7.

25. 
    
    
    
    26. 
        
        
        
        27. 
            
        
        
        
        
    
    
    
    


26. 
    
    
    
    29. 
        
        
        
        30. 
            
        
        
        
        
    
    
    
    


27. 
    
    
    
    32. 
        
        
        
        33. 
            
        
        
        
        
    
    
    
    


28. 
    
    
    
    35. 
        
        
        
        36. 
            
        
        
        
        
    
    
    
    


29. 
    
    
    
    38. 
        
        
        
        39. 
            
        
        
        
        
    
    
    
    


30. 
    
    
    
    41. 
        
        
        
        42. 
            
        
        
        
        
    
    
    
    


31. 
    
    
    
    44. 
        
    
    
    
    


32. 
    
    
    
    46. 
        
    
    
    
    


33. 
    
    
    
    48. 
        
    
    
    
    

49.Concept Check What are the two possible LCDs that could be used for the sum

?

50.Concept Check If one form of the correct answer to a sum or difference of rational

expressions is , what would an alternative form of the answer be if the denominator

is?

Add or subtract. Write each answer in lowest terms. See Examples 5 and 8.

51. 
    
    
    
    52. 
        
        
        
        53. 
            
        
        
        
        
    
    
    
    
    
    
    • 1
      1 - y
    
    
    
    

• 
  

4 y- 3

y- 1

10

m- 2

+

5

2 - m

4

x- 5

+

6

5 - x

3 - k

4

k- 3

10

m- 2 +

5

2 - m^

2 p

p- 3

+

2 +p

p

• 
  
  
  
  • 6
    p^2 - 3 p
  
  
  
  

t

t+ 2

+

5 - t

t

• 
  

4

t^2 + 2 t

2 x

x^2 - 16

• 
  

3

x^2 + 8 x+ 16

4 y

y^2 - 1

• 
  

5

y^2 + 2 y+ 1

a

a^2 + 3 a- 4

+

4 a

a^2 + 7 a+ 12

4 m

m^2 + 3 m+ 2

+

2 m- 1

m^2 + 6 m+ 5

2 x

x- 1

+

• 4
  x^2 - 1

x

x- 2

+

• 8
  x^2 - 4

3

m+ 1

• 4
  m

1

k+ 4

• 2
  k

12

5 m^2

• 5
  m

7

3 p^2

• 2
  p

x+ 2

5 x

+

6 x+ 3

3 x

x+ 3

3 x

+

2 x+ 2

4 x

2 x- 6

4

+

x+ 5

6

x+ 1

6

+

3 x+ 3

9

3

2 x

+

3

7 x

6

5 x

+

9

2 x

• 
  

7

8

• 
  

3

2 a

• 
  

3

4

• 
  

1

2 x

20

9

• 
  

z

3

5

7

• r
  2

p

8

+

4

5

z

5

+

1

3

• 4
  y^2 - 16


• 
  


• y
  y^2 - 16

x

x^2 - 9

• 
  
  
  
  • 3
    x^2 - 9
  
  
  
  

r^2 - 8 r

r- 5

+

15

r- 5

y^2 - 3 y

y+ 3

+

• 18
  y+ 3

t^2

t- 3

+

• 3 t
  t- 3

x^2

x+ 5

+

5 x

x+ 5

x-y

2

• 
  

x+y

2

a+b

2

• 
  

a-b

2

4 x

x+ 2

• 
  

2 + 3 x

x+ 2

5 m

m+ 1

• 
  

1 + 4 m

m+ 1

a

a+b

+

b

a+b

x

x+y

+

y

x+y

6

t+ 3

• 
  

3

t+ 3

5

y+ 4

• 1
  y+ 4

5

p

+

12

p

4

m

+

7

m

446 CHAPTER 7 Rational Expressions and Applications

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