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: 23

Answer

$\dfrac{3x^{2}}{x^{2}-1}\div\dfrac{x^{5}}{(x+1)^{2}}=\dfrac{3(x+1)}{x^{3}(x-1)}$

Work Step by Step

$\dfrac{3x^{2}}{x^{2}-1}\div\dfrac{x^{5}}{(x+1)^{2}}$ Factor the denominator of the first fraction: $\dfrac{3x^{2}}{x^{2}-1}\div\dfrac{x^{5}}{(x+1)^{2}}=\dfrac{3x^{2}}{(x-1)(x+1)}\div\dfrac{x^{5}}{(x+1)^{2}}=...$ Evaluate the division of the two rational expressions and simplify by removing repeated factors in the numerator and the denominator: $...=\dfrac{3x^{2}(x+1)^{2}}{x^{5}(x-1)(x+1)}=\dfrac{3x^{2}(x+1)}{x^{5}(x-1)}=\dfrac{3(x+1)}{x^{3}(x-1)}$
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