Q. 8.109 - Intermediate Algebra

Question

In the following exercise ,simplify 

$\frac{\sqrt{p}+\sqrt{2}}{\sqrt{p}-\sqrt{2}}$

Step-by-Step Solution

Answer

$\frac{{(\sqrt{p}+\sqrt{2})}^2}{p-2}.$

Part (a) Step 1. Given information.

Given expression:

$\frac{\sqrt{p}+\sqrt{2}}{\sqrt{p}-\sqrt{2}}$

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 $\sqrt{p}+\sqrt{2}$.

$$\begin{gathered} \frac{\sqrt{p}+\sqrt{2}}{\sqrt{p}-\sqrt{2}}\times \frac{\sqrt{p}+\sqrt{2}}{\sqrt{p}+\sqrt{2}} \\ =\frac{{(\sqrt{p}+\sqrt{2})}^2}{p-2} \end{gathered}$$