Q. 8.106 - Intermediate Algebra

Question

In the following exercise ,simplify 

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

Step-by-Step Solution

Answer

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

Part (a) Step 1. Given information.

Given expression:

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

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 $4+\sqrt{6}$.

$$\begin{gathered} \frac{2}{4-\sqrt{6}}\times \frac{4+\sqrt{6}}{4+\sqrt{6}} \\ =\frac{2(4+\sqrt{6})}{4^2-{\sqrt{16}}^2} \\ =\frac{2(4+\sqrt{6})}{10} \\ =\frac{(4+\sqrt{6})}{5} \end{gathered}$$