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: 68

Answer

$\frac{x^{3}}{x^{2}+y^{2}}$

Work Step by Step

We multiply the right fraction by $\frac{xy}{xy}$. Then we form a common denominator and combine the fractions: $\displaystyle x-\frac{y}{\frac{x}{y}+\frac{y}{x}}=x-\frac{y}{\frac{x}{y}+\frac{y}{x}}\cdot\frac{xy}{xy}=x-\frac{xy^{2}}{x^{2}+y^{2}}=\frac{x(x^{2}+y^{2})}{x^{2}+y^{2}}-\frac{xy^{2}}{x^{2}+y^{2}}=\frac{x^{3}+xy^{2}-xy^{2}}{x^{2}+y^{2}}=\frac{x^{3}}{x^{2}+y^{2}}$
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