# How do you rationalize the denominator and simplify 2/(sqrt6-sqrt5)?

Refer to explanation

#### Explanation:

When you have a formula like $\sqrt{a} - \sqrt{b}$ in the denominator you multiply with $\sqrt{a} + \sqrt{b}$ so

$\frac{2}{\sqrt{6} - \sqrt{5}} = 2 \cdot \frac{\sqrt{6} + \sqrt{5}}{\left(\sqrt{6} - \sqrt{5}\right) \cdot \left(\sqrt{6} + \sqrt{5}\right)} = 2 \cdot \frac{\sqrt{6} + \sqrt{5}}{{\left(\sqrt{6}\right)}^{2} - {\left(\sqrt{5}\right)}^{2}} = 2 \cdot \frac{\sqrt{6} + \sqrt{5}}{6 - 5} = 2 \cdot \left(\sqrt{6} + \sqrt{5}\right)$

Remarks

We used the identity ${a}^{2} - {b}^{2} = \left(a - b\right) \cdot \left(a + b\right)$