Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.4 - Rational Expressions - 1.4 Exercises - Page 43: 69



Work Step by Step

$\dfrac{x^{-2}-y^{-2}}{x^{-1}+y^{-1}}$ Rewrite the fraction like this: $\dfrac{x^{-2}-y^{-2}}{x^{-1}+y^{-1}}=\dfrac{\dfrac{1}{x^{2}}-\dfrac{1}{y^{2}}}{\dfrac{1}{x}+\dfrac{1}{y}}=...$ Evaluate the substraction in the numerator and the sum in the denominator $...=\dfrac{\dfrac{y^{2}-x^{2}}{x^{2}y^{2}}}{\dfrac{y+x}{xy}}=...$ Evaluate the division: $...=\dfrac{xy(y^{2}-x^{2})}{x^{2}y^{2}(y+x)}=...$ Simplify: $...=\dfrac{y^{2}-x^{2}}{xy(y+x)}=\dfrac{(y-x)(y+x)}{xy(y+x)}=\dfrac{y-x}{xy}$
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