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: 35

Answer

$\dfrac{x^2-xy+y^2}{x^2+xy+y^2}$

Work Step by Step

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