Beginning Algebra, 11th Edition

448 CHAPTER 7 Rational Expressions and Applications

Perform the indicated operations, using the order of operations as necessary. See Section 1.1.

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        79. 
            
            
            
            80. 
                
            
            
            
            
        
        
        
        
    
    
    
    

5

7

5

3

3

2

7

4

3

8

1

4

5

6

2

3

PREVIEW EXERCISES

OBJECTIVES The quotient of two mixed numbers in arithmetic, such as can be written as

a fraction.

2 +

1

2

3 +

1

4

=

2

1

2

3

1

4

2

1

2

, 3

1

4

=

2 12 , 3 14 ,

Complex Fractions

7.5

1 Simplify a complex

fraction by writing

it as a division

problem (Method 1).

2 Simplify a complex

fraction by

multiplying

numerator and

denominator by the

least common

denominator

(Method 2).

We do this to

illustrate a

complex fraction.

In algebra, some rational expressions have fractions in the numerator, or denominator,

or both.

Complex Fraction

A quotient with one or more fractions in the numerator, or denominator, or both,

is called a complex fraction.

, , and Complex fractions

The parts of a complex fraction are named as follows.

2

p

• 
  

1

q

3

p

+

5

q

3 +x

5 -

2

x

3 x^2 - 5 x

6 x^2

2 x-

1

x

2 +

1

2

3 +

1

4

Numerator of complex fraction

Main fraction bar

⎧ Denominator of complex fraction

⎨

⎩

⎧

⎨

⎩

OBJECTIVE 1 Simplify a complex fraction by writing it as a division prob-

lem (Method 1).Since the main fraction bar represents division in a complex frac-

tion, one method of simplifying a complex fraction involves division.

Method 1 for Simplifying a Complex Fraction

Step 1 Write both the numerator and denominator as single fractions.

Step 2 Change the complex fraction to a division problem.

Step 3 Perform the indicated division.

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