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: 42

Answer

$\dfrac{3y}{3-x}\div\dfrac{12xy}{x^{2}-9}=-\dfrac{x+3}{4x}$

Work Step by Step

$\dfrac{3y}{3-x}\div\dfrac{12xy}{x^{2}-9}$ Factor the denominator of the second fraction: $\dfrac{3y}{3-x}\div\dfrac{12xy}{x^{2}-9}=\dfrac{3y}{3-x}\div\dfrac{12xy}{(x-3)(x+3)}=...$ Evaluate the division of the two rational expressions and simplify by removing the factors that appear both in the numerator and the denominator of the resulting expression. To eliminate $(3-x)$ and $(x-3)$, change the sign of the factor $(3-x)$ and also the sign of the fraction: $..=\dfrac{3y(x-3)(x+3)}{12xy(3-x)}=-\dfrac{3(x-3)(x+3)}{12x(x-3)}=-\dfrac{3(x+3)}{12x}=...$ $...=-\dfrac{x+3}{4x}$
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