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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. 8.106 (page 808)

In the following exercise ,simplify
$\frac{2}{4 - \sqrt{6}}$

Short Answer

Expert verified

$\frac{4 + \sqrt{6}}{5}$ .

Step by step solution

01

Part (a) Step 1. Given information.

Given expression:

$\frac{2}{4 - \sqrt{6}}$

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 $4 + \sqrt{6}$ .

$\frac{2}{4 - \sqrt{6}} 脳 \frac{4 + \sqrt{6}}{4 + \sqrt{6}} = \frac{2 (4 + \sqrt{6})}{4^{2} - {\sqrt{16}}^{2}} = \frac{2 (4 + \sqrt{6})}{10} = \frac{(4 + \sqrt{6})}{5}$

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