Algebra 1 Common Core Student Edition, Grade 8-9

Simplifying Rational

Expressions

Objective To simplify rational expressions

Common Core State Standards

Prepares fo r A-APR.D.7... add, subtract, multiply,

and divide rational expressions.

MP 1, MP 2, MP 3, M P 4

Get more volume

fo r your su rface

area. That's

efficient packaging.

fi " Getting Ready!

Which box uses less cardboard per cubic

inch o f space inside it? J u s tif y your

answ er. (Hint: How would comparing a box's

su rfa c e a re a to its volume help you answer

this question?)

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MATHEMATICAL p o ly n o m ia l

PRACTICES An expression of th e form po|ynoiT^iai is a rational expression.

Lesso n

Vocabulary

• rational
  expression
  excluded value

Esse n t i a l U n d e r st a n d i n g The sim plified form of a rational expression is like

th e simplified form of a num erical fraction. The n u m era to r an d d en o m in ato r have no

com m on factor o th er th a n 1. To simplify a rational expression, divide out com m on

factors from the n u m era to r an d denom inator.

Like a num erical fraction, a rational expression is u n d efin e d w h en the d en o m in ato r

is 0. A value of a variable for w hich a rational expression is u n d efin ed is an

excluded value.

Should you use the

simplified form to

find excluded values?

No. You must check the

original expression to see

which values o fx make

the denominator 0.

Pr o b l em 1 Simplifying a Rational Expression

What is the simplified form of 5x _JC^1 5? State any excluded values.

x — 1 x — 1

5x - 5 5(x - 1) Factor the denominator. The num erator cannot be factored.

Divide o ut the common factor x - 1.

Simplify.

The d en o m in ato r of th e original expression is 0 w h en x = 1. The sim plified form

is w here x # 1.

L < 9 G o t It? 1. W hat is th e simplified form of th e expression? State any excluded values.

a.21a k 18ri2 c 2» — 3 j 26c3 + 91c

7 a 3 4<2+8^6 n —^9

664 Chapter 11 Rat io nal Expressions and Funct ions

KLEI