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: 96

Answer

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

Work Step by Step

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