## College Algebra 7th Edition

Published by Brooks Cole

# 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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