Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 7 - Section 7.2 - Multiplying and Dividing Rational Expressions - Exercise Set: 41

Answer

$\dfrac{x^{2}-4}{24x}\div\dfrac{2-x}{6xy}=-\dfrac{y(x+2)}{4}$

Work Step by Step

$\dfrac{x^{2}-4}{24x}\div\dfrac{2-x}{6xy}$ Factor the numerator of the first fraction: $\dfrac{x^{2}-4}{24x}\div\dfrac{2-x}{6xy}=\dfrac{(x+2)(x-2)}{24x}\div\dfrac{2-x}{6xy}=...$ Evaluate the division of the two rational expressions and simplify by removing factors that appear both in the numerator and the denominator. To remove $(x-2)$ and $(2-x)$, change the sign of $(2-x)$, and the sign of the fraction: $...=\dfrac{6xy(x+2)(x-2)}{24x(2-x)}=-\dfrac{6xy(x+2)(x-2)}{24x(x-2)}=...$ $...=-\dfrac{6y(x+2)}{24}=-\dfrac{y(x+2)}{4}$
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