8.3 Dividing Rational Expressions

CORD Math

Mrs. Spitz

Fall 2006

Objective

• Divide rational expressions

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Assignment

• Pg. 317 #3-33 all

Introduction

• You should recall that two numbers whose product is 1 are called multiplicative inverses or reciprocals.

• To find the quotient of two fractions, you multiply by the reciprocal of the divisor.

3

4

3

2

4

3

3

2

9

8

You can use this same method to divide rational expressions.

Ex. 1: Find z

y

x5

y

z

xz

y

x55

xy

z

y

z

x

55

The reciprocal of isz

y

y

z

Ex. 2: Find ).1(1

2

x

x

x

1

1

1

2)1(

1

2

xx

xx

x

x 1xThe reciprocal of is1

1

x

)1)(1(

2

xx

x

1

22

x

x

Ex. 3: Find.

2 2222 yxyx

yx

yx

yx

yx

yxyx

yx

yx

yxyx

yx

yx

yx

22

222222

2

2

yx

yxyx

yx

yx

22

22

2

Multiply by the reciprocal.

yx

yxyx

yxyx

yx

))((

))((

Factor difference of squares and perfect square trinomial.

Cancel common factors.

= 1 All factors cancel leaving 1/1 or 1.