Question

In the following exercises, simplify.

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

Short answer

The answer is$\frac{{\left(\sqrt{m}-\sqrt{3}\right)}^2}{m-3}$

Step-by-step solution

Step 1. Given

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

Step 2. Rationalize the denominators of the given expressions.

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