# How do you simplify 4 /(sqrt7 + sqrt 3)?

Apr 3, 2017

You multiply the both halves by $\sqrt{7} - \sqrt{3}$ and use the special product $\left(A + B\right) \left(A - B\right) = {A}^{2} - {B}^{2}$

#### Explanation:

$= \frac{4}{\sqrt{7} - \sqrt{3}} \times \frac{\sqrt{7} - \sqrt{3}}{\sqrt{7} - \sqrt{3}}$

$= \frac{4 \left(\sqrt{7} - \sqrt{3}\right)}{\left(\sqrt{7} + \sqrt{3}\right) \left(\sqrt{7} - \sqrt{3}\right)}$

$= \frac{4 \left(\sqrt{7} - \sqrt{3}\right)}{{\sqrt{7}}^{2} - {\sqrt{3}}^{2}} = \frac{4 \left(\sqrt{7} - \sqrt{3}\right)}{7 - 3} =$

$= \frac{\cancel{4} \left(\sqrt{7} - \sqrt{3}\right)}{\cancel{4}} = \sqrt{7} - \sqrt{3}$