Question

In the following exercises, simplify.

$\frac{\sqrt{3}}{\sqrt{m}-\sqrt{5}}$

Short answer

The answer is$\frac{\sqrt{3}\left(\sqrt{m}+\sqrt{5}\right)}{m-5}$

Step-by-step solution

Step 1. Given

The expression is$\frac{\sqrt{3}}{\sqrt{m}-\sqrt{5}}$

Step 2. Rationalize the denominators of the given expressions.

$$\begin{gathered} \frac{\sqrt{3}}{\sqrt{m}-\sqrt{5}} \\ =\frac{\sqrt{3}}{\sqrt{m}-\sqrt{5}}\times \frac{\sqrt{m}+\sqrt{5}}{\sqrt{m}+\sqrt{5}} \\ =\frac{\sqrt{3}\left(\sqrt{m}+\sqrt{5}\right)}{{\left(\sqrt{m}\right)}^2-{\left(\sqrt{5}\right)}^2} \\ =\frac{\sqrt{3}\left(\sqrt{m}+\sqrt{5}\right)}{m-5} \end{gathered}$$