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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 8.107 (page 809)

In the following exercise ,simplify
$\frac{\sqrt{5}}{\sqrt{x} + \sqrt{2}}$

Short Answer

Expert verified

$\frac{\sqrt{5} (\sqrt{x} - \sqrt{2})}{x - 2}$ .

Step by step solution

01

Part (a) Step 1. Given information.

Given expression:

$\frac{\sqrt{5}}{\sqrt{x} + \sqrt{2}}$

02

Part (a) Step 2. Finding solution.

Finding the solution.

Multiply numerator and denominator by the same factor i.e conjugate of denominator.

Multiply numerator and denominator $\sqrt{x} - \sqrt{2}$ .

$\frac{\sqrt{5}}{\sqrt{x} + \sqrt{2}} 脳 \frac{\sqrt{x} - \sqrt{2}}{\sqrt{x} - \sqrt{2}} = \frac{\sqrt{5} (\sqrt{x} - \sqrt{2})}{x - 2}$

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