Beginning Algebra, 11th Edition

Dividing Rational Expressions

Divide. Write the answer in lowest terms.

Multiply by the reciprocal.

Multiply numerators.

Multiply denominators.

Factor the numerator.

or Lowest terms;

NOW TRY

Dividing Rational Expressions (Factors Are Opposites)

Divide. Write the answer in lowest terms.

Multiply by the reciprocal.

Multiply numerators.

Multiply denominators.

Factor; and are opposites.

From Section 7.1,

or Distribute in the numerator.Rewrite as.

NOW TRY

In summary, use the following steps to multiply or divide rational expressions.

• m+ 2 2 - m

2 - m - 1

2 m 1 m+ 12

=

• m+ 2
  2 m 1 m+ 12

,

1 - m

= m- 1 =-1.

• 11 m- 22
  2 m 1 m + 12

= 1 - m m- 1

1 m+ 221 m - 2211 - m 2

1 m+ 121 m- 1212 m 21 m+ 22

=

1 m^2 - 4211 - m 2

1 m^2 - 1212 m^2 + 4 m 2

=

m^2 - 4

m^2 - 1

#^1 - m

2 m^2 + 4 m

m^2 - 4

m^2 - 1

,

2 m^2 + 4 m

1 - m

EXAMPLE 7

• a
  b =-

a

• b

2 x

1 x+ 322

=

• 2 x
  1 x+ 322

,

=

• 2 x 1 x+ 221 x- 22
  1 x+ 321 x- 221 x+ 221 x+ 32

=

• 2 x 1 x^2 - 42
  1 x+ 321 x- 221 x+ 221 x+ 32

=

x^2 - 4

1 x+ 321 x- 22

# -^2 x

1 x+ 221 x+ 32

x^2 - 4

1 x+ 321 x- 22

,

1 x+ 221 x+ 32

• 2 x

EXAMPLE 6

432 CHAPTER 7 Rational Expressions and Applications

NOW TRY
EXERCISE 6
Divide. Write the answer in
lowest terms.

t^2 - 25

1 t+ 521 t+ 22

1 t+ 221 t- 52

• 4 t
  ,

NOW TRY ANSWERS

6. or -

1 t+ 222

4 t^

1 t+ 222

• 4 t^ ,

NOW TRY
EXERCISE 7
Divide. Write the answer in
lowest terms.

7 - x

2 x+ 6

,

x^2 - 49

x^2 + 6 x+ 9

7. or - x+^3
   21 x+ 72

• x- 3
  21 x+ 72
  ,

Multiplying or Dividing Rational Expressions

Step 1 Note the operation.If the operation is division, use the definition

of division to rewrite it as multiplication.

Step 2 Multiplynumerators and multiply denominators.

Step 3 Factorall numerators and denominators completely.

Step 4 Write in lowest termsusing the fundamental property.

Note: Steps 2 and 3 may be interchanged based on personal preference.

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