College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.5 - Rational Expressions - R.5 Exercises - Page 47: 37



Work Step by Step

The given expression, $ \dfrac{xz-xw+2yz-2yw}{z^2-w^2}\cdot\dfrac{4z+4w+xz+wx}{16-x^2} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{(xz-xw)+(2yz-2yw)}{z^2-w^2}\cdot\dfrac{(4z+4w)+(xz+wx)}{16-x^2} \\\\= \dfrac{x(z-w)+2y(z-w)}{(z-w)(z+w)}\cdot\dfrac{4(z+w)+x(z+w)}{(4+x)(4-x)} \\\\= \dfrac{(z-w)(x+2y)}{(z-w)(z+w)}\cdot\dfrac{(z+w)(4+x)}{(4+x)(4-x)} \\\\= \dfrac{(\cancel{z-w})(x+2y)}{(\cancel{z-w})(\cancel{z+w})}\cdot\dfrac{(\cancel{z+w})(\cancel{4+x})}{(\cancel{4+x})(4-x)} \\\\= \dfrac{x+2y}{4-x} .\end{array}
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