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: 69

Answer

$\frac{y-x}{xy}$

Work Step by Step

We form a common denominator for the fractions in the numerator and denominator. After combining them, we switch from division to multiplication by taking the reciprocal of the denominator. Then we factor and simplify. $\displaystyle \frac{x^{-2}-y^{-2}}{x^{-1}+y^{-1}}=\frac{\frac{1}{x^{2}}-\frac{1}{y^{2}}}{\frac{1}{x}+\frac{1}{y}}=\frac{\frac{y^{2}}{x^{2}y^{2}}-\frac{x^2}{x^2y^2}}{\frac{y}{xy}+\frac{x}{xy}}=\frac{y^{2}-x^{2}}{x^{2}y^{2}}.\frac{xy}{y+x}=\frac{(y-x)(y+x)xy}{x^{2}y^{2}(y+x)}=\frac{y-x}{xy}$
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