Beginning Algebra, 11th Edition

(b)

Factor the denominator in each rational expression.

12 p

p 1 p+ 82

=

?

p 1 p+ 821 p- 42

12 p

p^2 + 8 p

=

?

p^3 + 4 p^2 - 32 p

438 CHAPTER 7 Rational Expressions and Applications

=p 1 p+ 821 p- 42

=p 1 p^2 + 4 p- 322

p^3 + 4 p^2 - 32 p

The factor is missing, so multiply by

Fundamental property

Multiply numerators.

Multiply denominators.

Multiply the factors. NOW TRY

NOTE While it is beneficial to leave the denominator in factored form, we multi-

plied the factors in the denominator in Example 5to give the answer in the same

form as the original problem.

=

12 p^2 - 48 p

p^3 + 4 p^2 - 32 p

=

12 p 1 p- 42

p 1 p+ 821 p- 42

12 p

p^2 + 8 p

=

12 p

p 1 p+ 82

#p-^4

p- 4

p- 4

p- 4.

12 p

p- (^4) p 1 p+ 82
Complete solution available
on the Video Resources on DVD
Concept Check Choose the correct response in Exercises 1–4.
1.Suppose that the greatest common factor of xand yis 1. What is the least common
denominator for and?
A.x B.y C.xy D. 1
2.If xis a factor of y, what is the least common denominator for and?
A.x B.y C.xy D. 1
3.What is the least common denominator for and?
A. 40 B. 2 C. 20 D.none of these
4.Suppose that we wish to write the fraction with denominator
By what must we multiply both the numerator and the denominator?
A. B. C. D.
Find the LCD for the fractions in each list. See Examples 1–3.

5. 
   
   
   
   6. 
      
      
      
      7. 
         
      
      
      
      
   
   
   
   


6. 
   
   
   
   9. 
      
      
      
      10. 
          
      
      
      
      
   
   
   
   


7. 
   
   
   
   12. 
       
       
       
       13. 
           
       
       
       
       
   
   
   
   


8. 
   
   
   
   15. 
       
       
       
       16. 
           
       
       
       
       
   
   
   
   

5

49 t^6

6

35 t^2

,

7

12 r^5

5

21 r^3

,

7

10 m^4

4

25 m^3

,

55

36 y^4

17

15 y^2

,

11

4 k

• 14
  15 k
  ,

13

6 p

• 2
  5 p
  ,

14

m^8

12

m^7

,

8

x^5

9

x^2

,

1

360

21

300

,

17

250

,

43

180

23

120

,

17

100

,

13

25

9

10

,

21

20

7

15

,

1 x- 421 y- 32 1 x- 422 x- 4 1 x- 4221 y- 32

1 x- 4231 y- 322.

1

1 x- 4221 y- 32

1

2

9

20

1

y

1

x

1

y

1

x

NOW TRY
EXERCISE 5
Rewrite each rational expres-
sion with the indicated
denominator.

(a)

(b)
?
t^3 + 12 t^2 + 32 t

2 t- 1

t^2 + 4 t

=

8 k

5 k- 2

=

?

25 k- 10

NOW TRY ANSWERS

5. (a)

(b)^2 t^

(^2) + 15 t- 8
t^3 + 12 t^2 + 32 t
40 k
25 k- 10
7.3 EXERCISES
http://www.ebook777.com
http://www.ebook777.com