Q. 8.108 - Intermediate Algebra

Question

In the following exercise ,simplify 

$\frac{\sqrt{10}}{\sqrt{y}-\sqrt{3}}$

Step-by-Step Solution

Answer

$\frac{\sqrt{10}(\sqrt{y}+\sqrt{3})}{y-3}$.

Part (a) Step 1. Given information.

Given expression:

$\frac{\sqrt{10}}{\sqrt{y}-\sqrt{3}}$

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 $\sqrt{y}+\sqrt{3}$.

$$\begin{gathered} \frac{\sqrt{10}}{\sqrt{y}-\sqrt{3}}\times \frac{\sqrt{y}+\sqrt{3}}{\sqrt{y}+\sqrt{3}} \\ =\frac{\sqrt{10}(\sqrt{y}+\sqrt{3})}{y-3} \end{gathered}$$