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: 21

Answer

$\dfrac{(x-6)(x+4)}{4x}\div\dfrac{2x-12}{8x^{2}}=x(x+4)$

Work Step by Step

$\dfrac{(x-6)(x+4)}{4x}\div\dfrac{2x-12}{8x^{2}}$ Take out common factor $2$ in the numerator of the second fraction: $\dfrac{(x-6)(x+4)}{4x}\div\dfrac{2x-12}{8x^{2}}=\dfrac{(x-6)(x+4)}{4x}\div\dfrac{2(x-6)}{8x^{2}}=...$ Evaluate the division of the two rational expressions: $...=\dfrac{8x^{2}(x-6)(x+4)}{8x(x-6)}=...$ Simplify by removing repeated factors in the numerator and the denominator: $...=\dfrac{8x^{2}(x+4)}{8x}=x(x+4)$
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