Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 6 - Section 6.1 - Rational Expressions and Functions; Multiplying and Dividing - Exercise Set - Page 417: 138

Answer

It doesn't make sense.

Work Step by Step

We have to perform the division: $$\dfrac{3x}{x+2}\div\dfrac{(x+2)^2}{x-4}.$$ In the beginning we transform division into multiplication, so the "common factor" $(x+2)$ is no longer common: $$\dfrac{3x}{x+2}\div\dfrac{(x+2)^2}{x-4}=\dfrac{3x}{x+2}\cdot\dfrac{x-4}{(x+2)^2}.$$ The factors $(x+2)$ and $(x+2)^2$ are both in the denominator, so we cannot simplify them! The given statement doesn't make sense.
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