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: 46

Answer

$\dfrac{9x+18}{4x^{2}-3x}\cdot\dfrac{4x^{2}-11x+6}{x^{2}-4}=\dfrac{9}{x}$

Work Step by Step

$\dfrac{9x+18}{4x^{2}-3x}\cdot\dfrac{4x^{2}-11x+6}{x^{2}-4}$ Factor both rational expressions completely: $\dfrac{9x+18}{4x^{2}-3x}\cdot\dfrac{4x^{2}-11x+6}{x^{2}-4}=\dfrac{9(x+2)}{x(4x-3)}\cdot\dfrac{(4x-3)(x-2)}{(x+2)(x-2)}=...$ Evaluate the product of the two rational expressions and simplify by removing the factors that appear both in the numerator and the denominator of the resulting expression: $...=\dfrac{9(x+2)(4x-3)(x-2)}{x(4x-3)(x+2)(x-2)}=\dfrac{9}{x}$
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