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: 81

Answer

$\frac{x+2}{(1+x)^{3/2}}$

Work Step by Step

We factor out $(1+x)^{-1/2}$, remembering that $(1+x)=(1+x)^{-1/2}*(1+x)^{1/2}$: $\displaystyle \frac{2(1+x)^{1/2}-x(1+x)^{-1/2}}{1+x}=\frac{(1+x)^{-1/2}[2(1+x)-x]}{1+x}=\frac{x+2}{(1+x)^{3/2}}$
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