College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.7 - Rational Expressions - P.7 Exercises: 67

Answer

$-xy$

Work Step by Step

We form a common denominator for both fractions and add them. Then we switch division to multiplication by taking the reciprocal of the bottom fraction. Finally we simplify: $\displaystyle \frac{\frac{x}{y}-\frac{y}{x}}{\frac{1}{x^2}-\frac{1}{y^2}}=\frac{\frac{x^{2}-y^{2}}{xy}}{\frac{y^{2}-x^{2}}{x^{2}y^{2}}}=\frac{x^{2}-y^{2}}{xy}*\frac{x^{2}y^{2}}{y^{2}-x^{2}}=\frac{xy}{-1}=-xy$
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