Algebra 1 Common Core Student Edition, Grade 8-9

Objectives To m ultiply an d divide rational expressions

To sim plify co m p le x fractio n s

— -.

' Getting Ready!

Solve a simpler

problem. U se a

value fo r x t o

understand w hat

is g o in g on.

In the figure a t the right, the diameter of the

sphere is equal to th e edge length x o f th e cube.

W hat p erce n t of th e cube's volume is tak en up by

the sphere? Justify your reasoning.

MAIHEMATICAL

PRACTICES

Lesso n

Vocabulary

com plex fraction

M any problem s require finding pro d u cts a n d q uotients of rational expressions.

Essential U nderstanding You can m ultiply a n d divide rational expressions

using th e sam e properties you use to m ultiply a n d divide n um erical fractions.

If a, b, c, and d re p re s e n t p o ly n o m ia ls (w h ere b Y 0 and d + 0), th e n § * | = ■

Are products of

rational expressions

defined for all real

numbers?

No. The products may

have excluded values.

In part (A), the excluded

value is 0. In part (B), the

excluded values are 0

and - 3.

Problem 1 Multiplying Rational Expressions

What is the product? State any excluded values.

Q

Multiply numerators and multiply denominators.

= —i r a Simplify.

The p ro d u ct is w here a ± 0.

f l - T — 7. x — 5

x jc + 3

x — 7 x - 5 _ (x - 7)(x - 5) Multiply numerators and multiply denominators,

x x + 3 x(x + 3) Leave the product in factored form.

(x — 7)(x — 5)

The p ro d u c t is — v(J+" 3 )— ’ w h e r e x + 0 and x # -3.

% G o t It? 1. W hat is th e product? State any excluded values.

@ C om m on C ore State Standards

1 A 11 * | *_______ J r\!. * Jt_-. A-APR.D.7... add, subtract, multiply, and divide

Multiplying Qnd LxlVlding rational expressions.

I. MP 1, MP 2, MP 3, MP 4, MP 7

Rational Expressions

670 Chapter 11 Rat io nal Expressions and Funct ions