Intermediate Algebra (11th edition)

Concept Check As review, multiply or divide the rational numbers as indicated. Write
answers in lowest terms.

13. 
    
    
    
    14. 
        
        
        
        15. 
            
        
        
        
        
    
    
    
    

16. 17. 18.

19.Concept Check Rational expressions often can be written in lowest terms in seemingly
different ways. For example,

and

look different, but we get the second quotient by multiplying the first by in both the

numerator and denominator. To practice recognizing equivalent rational expressions,

match the expressions in parts (a) – (f ) with their equivalents in choices A–F.

(a) (b) (c) (d) (e) (f )

A. B. C. D. E. F.

20.Concept Check Which rational expressions equal

A. B. C. D. E. F.

21.Concept Check Identify the two termsin the numerator and the two termsin the

denominator of the rational expression , and write it in lowest terms.

22.Concept Check Which rational expression can be simplified?

A. B. C. D.

23.Concept Check Which rational expression is notequivalent to

A. B. C. D.

24.Concept Check Which two rational expressions equal?

A. B. C. D.

Write each rational expression in lowest terms. See Example 2.

25. 26. 27.

28. 29. 30.

31. 32. 33.

34. 35. 36.

37. 38. 39.

2 t+ 6

t^2 - 9

m 2 - 25

4 m- 20

t 2 - 9

3 t+ 9

2 x^2 - 5 x

16 x- 40

3 z^2 +z

18 z+ 6

5 r- 20

3 r- 12

6 m+ 18

7 m+ 21

4 x- 9

4

3 x+ 7

3

5 y^21 y+ 82

15 y 1 y- 82

4 x 1 x+ 32

8 x^21 x- 32

12 x+ 721 x- 12

12 x+ 3212 x+ 72

1 x+ 421 x- 32

1 x+ 521 x+ 42

y^31 y- 42

y^21 y- 42

x^21 x+ 12

x 1 x+ 12

2 x+ 3

• 2 x- 3

2 x+ 3

3 + 2 x

2 x- 3

3 - 2 x

2 x+ 3

2 x- 3

- 1

-

x- 3

x- 4

-

3 - x

4 - x

x+ 3

4 +x

3 - x

x- 4

x- 3

4 - x^?

x^2 - 5 x

x

x^2 +y^2

y^2

x^2 + 2

2

x^2 + 2

x^2

x^2 + 4 x

x+ 4

-

• x


• y


• x
  y

-

x

• y

x

y

x

• y


• x


• y


• xy?


• x- 3
  x- 4

x- 3

• x- 4


• x+ 3


• x+ 4

3 - x

• x- 4


• x- 3


• x- 4


• x- 3
  4 - x

x+ 3

4 - x

3 - x

x+ 4

x+ 3

x+ 4

x- 3

x- 4

x+ 3

x- 4

x- 3

x+ 4

- 1

• y+ 3
  5

y- 3

• 5

3

8

,

9

14

2

3

,

8

9

5

6

,

14

15

3

8

,

5

12

5

9

#^12

25

4

21

#^7

10

SECTION 7.1 Rational Expressions and Functions; Multiplying and Dividing 369