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: 95

Answer

$\frac{1}{\sqrt{x^{2}+1}+x}$

Work Step by Step

We simplify the fraction by multiplying through by $\sqrt{x^2+1}+x$ and using the fact that $(a-b)(a+b)=a^2-b^2$: $\displaystyle \sqrt{x^{2}+1}-x=\frac{\sqrt{x^{2}+1}-x}{1} \displaystyle *\frac{\sqrt{x^{2}+1}+x}{\sqrt{x^{2}+1}+x}=\frac{x^{2}+1-x^{2}}{\sqrt{x^{2}+1}+x}=\frac{1}{\sqrt{x^{2}+1}+x}$
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