# How do you rationalize the denominator and simplify 1/(sqrt5-3)?

May 3, 2016

$\frac{1}{\sqrt{5} - 3} = - \frac{\sqrt{5} + 3}{4}$

#### Explanation:

For expressions $\frac{\textrm{s o m e t h \in g}}{\sqrt{a} - b}$ we multiply the numerator and denominator by $\sqrt{a} + b$ so it matches the LHS of the formula $\left(x + y\right) \left(x - y\right) = {x}^{2} - {y}^{2}$.

$\frac{1}{\sqrt{5} - 3} = \frac{1}{\sqrt{5} - 3} \cdot \frac{\sqrt{5} + 3}{\sqrt{5} + 3} = \frac{\sqrt{5} + 3}{5 - 9} = - \frac{\sqrt{5} + 3}{4}$