Warm-Up
• Factor the following:
2x2 + 7x – 15
Product: -30 … (2)(-15)
Factor Pair: -3 , 10
BUILD: -3/2 10/2
(2x – 3) (x + 5)
Simplify: -3/2 , 5/1
Simplify, Multiply, and Divide
Rational Expressions
Unit 9: Rational Functions
TEXT: L11-4 Rational Expressions
pp.476-482
Essential Question
• How does factoring help me with multiplying
and dividing rational expressions?
Steps for Multiplying/Dividing Rational
Expressions
1. Factor numerator and denominator completely.
2. Turn any division into multiplication of the
reciprocal.
3. Cancel any like binomial factors that are in both
the numerator and denominator. (Note: only
factors can be cancelled – not added or subtracted
numbers.)
4. Write your simplified answer as a single fraction.
Leave in factored form.
Ex. 1: Simplify
1. Factor:
2. No Division
3. Cancel factors:
4. Write as fraction:
GCF
Factors
Cancel
One
power of
x cancels
Ex 2: Simplify
1. Factor numerator
by grouping and
denominator by
difference of
squares:
2. No Division
3. Cancel Factors
4. Write as fraction
Build Simplify Fix
Ex 3: Simplify
1. Factor:
2. No Division
3. Cancel Factors
4. Write as fraction
GCF
GCF
GCF
Ex 4: Simplify
1. Factor:
2. No Division
3. Cancel Factors
4. Write as fraction
Build Simplify Fix
Build Simplify Fix
Build Simplify Fix
Ex 5: Simplify
1. Factor:
2. Division so Multiply
by the Reciprocal
3. Cancel Factors
4. Write as fraction
Build Simplify Fix
Build Simplify Fix
Ex 6: Simplify
1. Factor:
2. Division so Multiply
by the Reciprocal
3. Cancel Factors
4. Write as fraction
GCF
GCF & Diff of Squares
Build Simplify Fix
Diff of Cubes
Ex 7: Simplify
Build Simplify Fix
1. Factor:
2. Division so Multiply
by the Reciprocal
3. Cancel Factors
4. Write as fraction
Diff of
Sq
GCF