Intermediate Algebra (11th edition)

7.2 Adding and Subtracting Rational

Expressions

Adding or Subtracting Rational Expressions

Step 1 If the denominators are the same,add or
subtract the numerators. Place the result over
the common denominator.
If the denominators are different,write all
rational expressions with the LCD. Then add or
subtract the numerators, and place the result
over the common denominator.

Step 2 Make sure that the answer is in lowest terms.

Subtract.

=

• 2 x- 16
  1 x+ 621 x+ 22

=

x+ 2 - 3 x- 18

1 x+ 621 x+ 22

=

x+ 2 - 31 x+ 62

1 x+ 621 x+ 22

=

x+ 2

1 x+ 621 x+ 22

-

31 x+ 62

1 x+ 621 x+ 22

1

x+ 6

-

3

x+ 2

CONCEPTS EXAMPLES

7.3 Complex Fractions

Simplifying a Complex Fraction

Method 1

Step 1 Simplify the numerator and denominator
separately, as much as possible.

Step 2 Multiply the numerator by the reciprocal of the
denominator.

Step 3 Then simplify the result.

Method 2

Step 1 Multiply the numerator and denominator of
the complex fraction by the least common
denominator of all fractions appearing in the
complex fraction.

Step 2 Then simplify the result.

Method 1 Method 2

=

y-x

xy

=

1 y-x 21 y+x 2

xy 1 y+x 2

=

y^2 - x^2

xy^2 +x^2 y

x^2 y^2 a

1

x^2

• 1
  y^2
  b

x^2 y^2 a

1

x

+

1

y

b

=

1

x^2

• 1
  y^2
  1
  x

• 1
  y

=

y-x

xy

=

1 y+x 21 y-x 2

x^2 y^2

# xy

y+x

,

y+x

xy

=

y^2 - x^2

x^2 y^2

y^2 - x^2

x^2 y^2

y+x

xy

=

y^2

x^2 y^2

• x^2
  x^2 y^2
  y
  xy

• x
  xy

=

1

x^2

• 1
  y^2
  1
  x

• 1
  y

(continued)

418 CHAPTER 7 Rational Expressions and Functions