Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 7 - Section 7.7 - Simplifying Complex Fractions - Exercise Set: 37

Answer

$\dfrac{\dfrac{s}{r}+\dfrac{r}{s}}{\dfrac{s}{r}-\dfrac{r}{s}}=\dfrac{s^{2}+r^{2}}{(s-r)(s+r)}$

Work Step by Step

$\dfrac{\dfrac{s}{r}+\dfrac{r}{s}}{\dfrac{s}{r}-\dfrac{r}{s}}$ Evaluate the sum indicated in the numerator and the substraction indicated in the denominator: $\dfrac{\dfrac{s}{r}+\dfrac{r}{s}}{\dfrac{s}{r}-\dfrac{r}{s}}=\dfrac{\dfrac{s^{2}+r^{2}}{rs}}{\dfrac{s^{2}-r^{2}}{rs}}=...$ Evaluate the division and simplify: $...=\dfrac{s^{2}+r^{2}}{rs}\div\dfrac{s^{2}-r^{2}}{rs}=\dfrac{rs(s^{2}+r^{2})}{rs(s^{2}-r^{2})}=\dfrac{s^{2}+r^{2}}{s^{2}-r^{2}}=...$ Factor the denominator to provide a more simplified answer: $...=\dfrac{s^{2}+r^{2}}{(s-r)(s+r)}$
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