# How do you simplify (sqrt7+sqrt3)/(sqrt7-sqrt3)?

Aug 29, 2016

${\left(\sqrt{7} + \sqrt{3}\right)}^{2} / 4$

#### Explanation:

Multiply both sides by $\frac{\sqrt{7} + \sqrt{3}}{\sqrt{7} + \sqrt{3}}$

$\frac{\sqrt{7} + \sqrt{3}}{\sqrt{7} - \sqrt{3}} \times \frac{\sqrt{7} + \sqrt{3}}{\sqrt{7} + \sqrt{3}}$

The bottom shows the factors of the difference of squares.

${\left(\sqrt{7} + \sqrt{3}\right)}^{2} / \left({\sqrt{7}}^{2} - {\sqrt{3}}^{2}\right) = {\left(\sqrt{7} + \sqrt{3}\right)}^{2} / \left(7 - 3\right)$

${\left(\sqrt{7} + \sqrt{3}\right)}^{2} / 4$