Beginning Algebra, 11th Edition

Simplifying a Complex Fraction (Method 1)

Simplify the complex fraction.

Write both second terms with

a denominator of

Distributive property

Combine like terms.

Multiply by the reciprocal of the

denominator (divisor).

= Divide out the common factor.

• 5 - 4 x
  4 +x

=

• 5 - 4 x
  x+ 2

#x+^2

4 +x

• 5 - 4 x
  x+ 2
  4 +x
  x+ 2

=

3 - 4 x- 8

x+ 2

2 +x+ 2

x+ 2

=

3 - 41 x+ 22

x+ 2

2 + 11 x+ 22

x+ 2

=

x+2.

3

x+ 2

41 x+ 22

x+ 2

2

x+ 2

+

11 x+ 22

x+ 2

=

3

x+ 2

• 4

2

x+ 2

+ 1

EXAMPLE 3

450 CHAPTER 7 Rational Expressions and Applications

NOW TRY
EXERCISE 3
Simplify the complex
fraction.

5 +

2

a- 3

1

a- 3

• 2

NOW TRY ANSWER

3.^57 a-- 213 a

Be careful

with signs.

Subtract in the numerator.

Add in the denominator.

NOW TRY

OBJECTIVE 2 Simplify a complex fraction by multiplying numerator and

denominator by the least common denominator (Method 2). Any expression

can be multiplied by a form of 1 to get an equivalent expression. Thus we can multi-

ply both the numerator and the denominator of a complex fraction by the same

nonzero expression to get an equivalent rational expression. If we choose the expres-

sion to be the LCD of all the fractions within the complex fraction, the complex frac-

tion can then be simplified. This is Method 2.

Method 2 for Simplifying a Complex Fraction

Step 1 Find the LCD of all fractions within the complex fraction.

Step 2 Multiply both the numerator and the denominator of the complex

fraction by this LCD using the distributive property as necessary.

Write in lowest terms.

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