Beginning Algebra, 11th Edition

Brain Busters The fractions in Exercises 47–52 are called continued fractions.Simplify by
starting at “the bottom” and working upward.

Simplify. See Section 1.8.

Solve each equation. See Sections 2.3 and 6.5.

57. 
    
    
    
    58. 
        
    
    
    
    


58. 61 z- 32 + 5 = 8 z- 3 60.k^2 + 3 k- 4 = 0

3 x+ 5 = 7 x+ 3 9 z+ 2 = 7 z+ 6

6 a

5 z^2

2

8 z

3

• 12 a b

11 p^2

3

9 p

4

b

8 a

3 r

4

+

9

8

9 a b

4 x

3

+

2

9

b

PREVIEW EXERCISES

q

6 +

8

4 + 4

2 q

7

• r
  4 -
  2
  6 + 2

r+

2

4 +

2

4 - 2

3 -

3

5 +

2

4 - 2

7 -

5

5 +

5

5 + 5

5 +

1

1 +

1

1 + 1

1 +

SECTION 7.5 Complex Fractions 455

Brain Busters Simplify each fraction.

39. 
    
    
    
    40. 1 +t -^1 - 56 t-^2
        1 - t -^1 - 72 t-^2
    
    
    
    

1 +x-^1 - 12 x-^2

1 - x-^1 - 20 x-^2

41.Concept Check In a fraction, what operation does the fraction bar represent?

42.Concept Check What property of real numbers justifies Method 2 of simplifying com-
plex fractions?

EXERCISES 43– 46

FOR INDIVIDUAL OR GROUP WORK

To find the average of two numbers, we add them and divide by 2. Suppose that we wish

to find the average of and. Work Exercises 43– 46 in order,to see how a complex

fraction occurs in a problem like this.

43.Write in symbols: The sum of and , divided by 2. Your result should be a

complex fraction.

44.Use Method 1 to simplify the complex fraction from Exercise 43.

45.Use Method 2 to simplify the complex fraction from Exercise 43.

46.Your answers in Exercises 44 and 45should be the same. Which method did you

prefer? Why?

5

6

3

8

5

6

3

8

RELATING CONCEPTS