Algebra 1 Common Core Student Edition, Grade 8-9

As Problem 1 indicates, pro d u cts of rational expressions m ay have excluded values. For

th e rest of this chapter, it is n o t necessary to state excluded values unless you are asked.

S om etim es th e p ro d u c t of two rational expressions m ay n o t be in sim plified form.

You m ay n e e d to divide out co m m o n factors.

Plan
What is a reasonable
first step?
When you multiply
rational expressions, a
reasonable first step is
to factor. Look for GCFs
to factor out. Then look
for quadratic expressions
that you can factor.

Problem 2 Using Factoring

What is the product — + 5 - l4x

x + 5

7x - 21 x2 + 3x - 10 ‘

14x _ x + 5 14x

7x - 21 x2 + 3x - 10 7{x - 3) (x + 5 )(x - 2) Factor denominators.

x-+'Tl 1 # 1-4 2x_______

^(x-3) 1(x-K5j(x-2) 7 a n d * + 5.

1 2 x

Divide out the common factors

x - 3 x - 2

. 2 x
(x — 3)(x - 2)

Simplify.

Multiply numerators and

m ultiply denominators. Leave

the product in factored form.

• A G o t It? 2. a. W hat is th e p ro d u c tx + 2 3 x x 2 + 3 x + 2 ^x
  b. Reasoning In Problem 2, su ppose you m ultiply th e n um erators
  and denominators before you factor. Will you still get th e sam e
  product? Explain.

You can also m ultiply a rational expression by a polynom ial. Leave th e p ro d u c t in

factored form.

Flap
How do you get
started?
Write the polynomial
as a rational expression
w ith denominator 1. Then
multiply the tw o rational
expressions.

Problem 3 Multiplying a Rational Expression by a Polynomial

What is the product * {rn2 + m — 6 )?

2 m + 5

3 m — 6 (m2 + m —^6 ) =

2m + 5 (m - 2)(m + 3)

3 (m - 2 ) 1

(2m + 5) (m “- 2)'(m + 3)

3j 1

(2m + 5 )(m + 3)

Factor.

Divide out the common

factor m-2.

Multiply. Leave the product in

factored form.

G o t It? 3. W hat is th e product?

a. • (6x2 - 13* + 6) b.x2 + 2x + 1X2 - 1 (x2 + 2x — 3)

Recall th a t § ^ § = § * w here b + 0, c =£ 0, an d d ¥= 0. W hen you divide rational

expressions, first rew rite th e q u o tien t as a p ro d u c t using th e reciprocal before dividing

out co m m o n factors.

£ PowerAlgebra.com JU Lesson 11-2 Multiplying and Dividing Rational Expressions 671

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