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: 47

Answer

$\dfrac{8n^{2}-18}{2n^{2}-5n+3}\div\dfrac{6n^{2}+7n-3}{n^{2}-9n+8}=\dfrac{2(n-8)}{3n-1}$

Work Step by Step

$\dfrac{8n^{2}-18}{2n^{2}-5n+3}\div\dfrac{6n^{2}+7n-3}{n^{2}-9n+8}$ Factor both rational expressions completely: $\dfrac{2(4n^{2}-9)}{(n-1)(2n-3)}\div\dfrac{(2n+3)(3n-1)}{(n-1)(n-8)}=...$ $...=\dfrac{2(2n-3)(2n+3)}{(n-1)(2n-3)}\div\dfrac{(2n+3)(3n-1)}{(n-1)(n-8)}=...$ 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: $...=\dfrac{2(2n-3)(2n+3)(n-1)(n-8)}{(n-1)(2n-3)(2n+3)(3n-1)}=\dfrac{2(n-8)}{3n-1}$
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