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: 28

Answer

$\dfrac{x-3}{2-x}\div\dfrac{x^{2}+3x-18}{x^{2}+2x-8}=-\dfrac{x+4}{x+6}$

Work Step by Step

$\dfrac{x-3}{2-x}\div\dfrac{x^{2}+3x-18}{x^{2}+2x-8}$ Factor the second fraction completely: $\dfrac{x-3}{2-x}\div\dfrac{x^{2}+3x-18}{x^{2}+2x-8}=\dfrac{x-3}{2-x}\div\dfrac{(x+6)(x-3)}{(x+4)(x-2)}=...$ Evaluate the division of the two rational expressions: $...=\dfrac{(x-3)(x+4)(x-2)}{(2-x)(x+6)(x-3)}=...$ Simplify by removing repeated factors in the numerator and the denominator. To remove $(x-2)$ and $(2-x)$, change the sign of the factor $(2-x)$ and also change the sign of the fraction: $...=\dfrac{(x+4)(x-2)}{(2-x)(x+6)}=-\dfrac{(x+4)(x-2)}{(x-2)(x+6)}=-\dfrac{x+4}{x+6}$
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