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: 48

Answer

$\dfrac{36n^{2}-64}{3n^{2}-10n+8}\div\dfrac{3n^{2}-5n-12}{n^{2}-9n+14}=\dfrac{4(n-7)}{n-3}$

Work Step by Step

$\dfrac{36n^{2}-64}{3n^{2}-10n+8}\div\dfrac{3n^{2}-5n-12}{n^{2}-9n+14}$ Factor both rational expressions completely: $\dfrac{4(9n^{2}-16)}{(3n-4)(n-2)}\div\dfrac{(3n+4)(n-3)}{(n-2)(n-7)}=...$ $...=\dfrac{4(3n-4)(3n+4)}{(3n-4)(n-2)}\div\dfrac{(3n+4)(n-3)}{(n-2)(n-7)}=...$ 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: $...=\dfrac{4(3n-4)(3n+4)(n-2)(n-7)}{(3n-4)(n-2)(3n+4)(n-3)}=\dfrac{4(n-7)}{n-3}$
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