Algebra 1 Common Core Student Edition, Grade 8-9

A diagram can help

you understand

th is situation. U se

a straigh t path.

"C

Getting Ready!

Geb can run th e d istance betw een his

house and Katy's in 20 min. Katy can

bicycle to Geb's house in 10 min. Geb

runs tow ard Katy's house while Katy

bicycles toward Geb's house. How long

will it be b e fo re th e y m eet on th e

road? Justify your reasoning.

MATHEMATICAL

PRACTICES

Lesson
Vocabulary
rational equatio n

A ratio n al eq u atio n is a n e q u a tio n th a t contains one or m ore rational expressions.

Esse n t i a l U n d e r st a n d i n g You can solve a rational eq u a tio n by first m ultiplying

each side of th e eq u a tio n by th e LCD. W hen each side of a rational e q u a tio n is a single

rational expression, you can solve th e eq u a tio n using th e Cross P roducts Property.

@ Common Core State Standards

A-CED.A.1 Create equations... in one variable and use

them to solve problems. Include equations arising fro m...

sim ple r a tio n a l... functions. Also A-REI.A.2

MP1, MP2, MP3, MP4

Objective To solve rational eq u atio n s a n d proportions

Solving Rational

Equations

Plan

Solving Equations W ith Rational Expressions

Have you seen an

equation like this

before?

Yes. In Lesson 2-3, you

solved equations that

contained fractions.

As you did there, you

can clear the fractions

from the equation by

multiplying by a common

denominator.

W hat is th e so lu tio n o f ^ ^ C heck th e so lu tio n.

5 ____]_ = J _

12 2 x 3x

12 x(l 2 2 x) 12x (3x)

l ^ x f ^ y - Distributive Property

5x — 6 = 4 Simplify.

5x= 10

x = 2

The denom inators are 1 2 ,2x, and 3x. The LCD is 12x.

M u ltip ly each side by 12x.

Add 6 to each side.

Divide each side by 5.

Che£k ft-2 ^ -3k Seeifx = 2makeS^

1 1 „

12 2 x - 3 x t r u e -

c

Po w er A lg eb r a.co m Lesson 11-5 So l v i n g Ra t i o n a l Eq u a t i o n s^691