Beginning Algebra, 11th Edition

(c)

Write as a division problem.

Multiply by the reciprocal.

Multiply and then factor.

= Divide out the common factors.

x+ 3

x- 2

=

1 x+ 221 x+ 321 x- 32

1 x- 321 x+ 221 x- 22

=

x+ 2

x- 3

#x

(^2) - 9
x^2 - 4

=

x+ 2

x- 3

,

x^2 - 4

x^2 - 9

x+ 2

x- 3

x^2 - 4

x^2 - 9

SECTION 7.5 Complex Fractions 453

NOW TRY
EXERCISE 6
Simplify each complex fraction.

(a)

(b)

9 y^2 - 16

y^2 - 100

3 y- 4

y+ 10

1 -

2

x

• 15
  x^2
  1 +^5
  x
  +^6
  x^2

NOW TRY ANSWERS

6. (a)xx+- 25 (b)y^3 y-+ 104

This is a quotient of two

rational expressions.

Use Method 1.

NOW TRY

Complete solution available
on the Video Resources on DVD 1.Concept Check Consider the complex fraction. Answer each part, outlining

Method 1 for simplifying this complex fraction.

(a)To combine the terms in the numerator, we must find the LCD of and. What is

this LCD? Determine the simplified form of the numerator of the complex fraction.

(b)To combine the terms in the denominator, we must find the LCD of and. What is

this LCD? Determine the simplified form of the denominator of the complex fraction.

(c)Now use the results from parts (a) and (b) to write the complex fraction as a division

problem using the symbol .

(d)Perform the operation from part (c) to obtain the final simplification.

2.Concept Check Consider the complex fraction given in Exercise 1:. Answer

each part, outlining Method 2 for simplifying this complex fraction.

(a)We must determine the LCD of all the fractions within the complex fraction. What is

this LCD?

(b)Multiply every term in the complex fraction by the LCD found in part (a), but do not

yet combine the terms in the numerator and the denominator.

(c)Combine the terms from part (b) to obtain the simplified form of the complex fraction.

3.Which complex fraction is equivalent to? Answer this question without showing

any work, and explain your reasoning.

A. B. C. D.

4.Only one of these choices is equal to. Which one is it? Answer this question without

showing any work, and explain your reasoning.

A. B. C. D.-

1

12

• 
  

9

5

• 
  

5

9

5

9

1

3 +

1

12

1

2 +

1

4

• 2 +^14


• 3 +^12


• 2 -^14


• 3 -^12

2 -^14

• 3 +^12

2 +^14

3 +^12

2 -^14

3 -^12

3

2 -

4

3

1

6 -

5

12

5

12

1

6

4

3

3

2

3

2 -

4

3

1

6 -

5

12

7.5 EXERCISES