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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 9: Q 786 (page 1154)

In the following exercises, rationalize the denominator.
$\frac{\sqrt{3}}{\sqrt{x} + \sqrt{5}}$

Short Answer

Expert verified

The simplification of the given expression $\frac{\sqrt{3}}{\sqrt{x} + \sqrt{5}}$ is $\frac{\sqrt{3 x} - \sqrt{15}}{x - 5}$

Step by step solution

01

Step 1. Given information

Given expression is $\frac{\sqrt{3}}{\sqrt{x} + \sqrt{5}}$

02

Step 2. Simplify by rationalizing the denominator

$\frac{\sqrt{3}}{\sqrt{x} + \sqrt{5}} = \frac{\sqrt{3}}{\sqrt{x} + \sqrt{5}} 脳 \frac{\sqrt{x} - \sqrt{5}}{\sqrt{x} - \sqrt{5}} = \frac{\sqrt{3} (\sqrt{x} - \sqrt{5})}{(\sqrt{x} + \sqrt{5}) (\sqrt{x} - \sqrt{5})} = \frac{\sqrt{3 x} - \sqrt{15}}{x - 5}$

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