### 8.3 Dividing Rational Expressions CORD Math Mrs. Spitz Fall 2006 Objective • Divide rational expressions.

```8.3 Dividing Rational
Expressions
CORD Math
Mrs. Spitz
Fall 2006
Objective
• Divide rational expressions
Upcoming
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8.3 Friday 10/20
8.4 Monday 10/23
8.5 Tuesday/Wednesday – Skip 8.6
8.7 Thursday 10/26
8.8 Friday 10/27
8.9 Monday 10/30
8.10 Tuesday/Wed
Chapter 8 Review Wed/Thur
Chapter 8 Test Friday
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
You can use this same method
divisor.
2 3 2 4
  
3 4 3 3
8

9
to divide rational expressions.
5 y
Ex. 1: Find 
x z
5 y 5 z
  
x z x y
5 z 5z
 
x y xy
The reciprocal of
y
z
is
z
y
Ex. 2: Find
2x
 ( x  1).
x 1
2x
2x
1
 ( x  1) 

x 1
x 1 x 1
The reciprocal of
2x

( x  1)(x  1)
2x
 2
x 1
x 1
is
1
x 1
Ex. 3: Find
x y
x y
 2
.
2
2
x y
x  2 xy  y 2
x y
x y
x  y x 2  2 xy  y 2
 2
 2

2
2
2
2
x y
x  2 xy  y
x y
x y
x y
x 2  2 xy  y 2
 2

2
x y
x y
x y
( x  y )(x  y )


( x  y )(x  y )
x y
=1
Multiply by the reciprocal.
Factor difference of
squares and perfect
square trinomial.
Cancel common factors.
All factors cancel leaving 1/1 or 1.
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