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: 36



Work Step by Step

The given expression, $ \dfrac{x^2-y^2}{(x-y)^2}\cdot\dfrac{x^2-xy+y^2}{x^2-2xy+y^2}\div\dfrac{x^3+y^3}{(x-y)^4} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{x^2-y^2}{(x-y)^2}\cdot\dfrac{x^2-xy+y^2}{x^2-2xy+y^2}\cdot\dfrac{(x-y)^4}{x^3+y^3} \\\\= \dfrac{(x+y)(x-y)}{(x-y)^2}\cdot\dfrac{x^2-xy+y^2}{(x-y)(x-y)}\cdot\dfrac{(x-y)^4}{(x+y)(x^2-xy+y^2)} \\\\= \dfrac{(\cancel{x+y})(x-y)}{(x-y)^2}\cdot\dfrac{\cancel{x^2-xy+y^2}}{(x-y)(x-y)}\cdot\dfrac{(x-y)^4}{(\cancel{x+y})(\cancel{x^2-xy+y^2})} \\\\= \dfrac{(x-y)^5}{(x-y)^4} \\\\= \dfrac{\cancel{(x-y)^4}(x-y)}{\cancel{(x-y)^4}} \\\\= x-y .\end{array}
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