College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter R - Section R.7 - Rational Expressions - R.7 Assess Your Understanding: 23

Answer

$\dfrac{8}{3x}; x \ne 0,2$

Work Step by Step

The given expression is equivalent to: $=\dfrac{4x-8}{-3x} \cdot \dfrac{12}{-6x+12}$ Factor each polynomial completely to obtain: $=\dfrac{2(2)(x-2)}{-3(x)} \cdot \dfrac{2(2)(3)}{-6(x-2)} \\=\dfrac{2(2)(x-2)}{-3(x)} \cdot \dfrac{2(2)(3)}{-2(3)(x-2)}$ Cancel the common factors to obtain: $\require{cancel} \\\\=\dfrac{2\cancel{(2)}\cancel{(x-2)}}{-3(x)} \cdot \dfrac{2(2)\cancel{(3)}}{-\cancel{2}\cancel{(3)}\cancel{(x-2)}} \\=\dfrac{2(2)(2)}{-3(x)(-1)} \\=\dfrac{8}{3x}; x \ne 0,2$
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