Algebra 1 Common Core Student Edition, Grade 8-9

Adding and Subtracting

Rational Expressions

Objective To ad d an d subtract rational expressions

Common Core State Standards

... add, subtract, multiply, and divide
expressions.
MP 1, MP 2, MP 3, MP 4

f| j Getting Ready! x C

Each dog eats part

of the dog food in

a bag ev ery day.

The question is

how to m ake th e

parts add up.

MATHEMATICAL

PRACTICES

T h re e dogs all e a t th e same dog food. The number of days it ta k e s

each dog to finish one bag o f food is shown below. How many bags of

food will it ta k e to fe e d all th r e e dogs f o r two weeks? Explain.

Time to Finish a Bag of Dog Food

MB

-mmm.....”1

Scruffy Oscar Gus

Essential U nderstanding You can use the sam e rules to ad d an d subtract

rational expressions th at you use to ad d an d subtract n um erical fractions.

You can add the n u m erato rs of rational expressions w ith like denom inators. If a, b, and

c r e p r e s e n t p o l y n o m i a l s ( w i t h c =A 0), th e n § + f =

Once you are

comfortable adding

rational expressions with

like denominators, you

can add the numerators

and simplify all in one

step.

Adding Expressions W ith Like Denominators

What is the sum?

□ — + —+ 3y

4 7 _ 4 + 7

3}' 3y 3 y

_ 11

3y

n 3r , x

Add the numerators.

Simplify the numerator.

'x - 2

3x +

x - 2

X 3x + x

x — 2

4x

x — 2

* G o t It? 1. W hat is the

Add the numerators.

Simplify the numerator.

sum3a - 4 3a — 4 ‘^2 a^3 a

684 C h a p t e r 11 Rat io nal Expressions and Funct ions

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