# How do you rationalize the denominator for 5/(sqrt6+sqrt5)?

Multiply the top and bottom by $\setminus \sqrt{6} - \setminus \sqrt{5}$ to get $\frac{5}{\setminus \sqrt{6} + \setminus \sqrt{5}} = \setminus \frac{5 \left(\setminus \sqrt{6} - \setminus \sqrt{5}\right)}{6 - 5} = 5 \setminus \sqrt{6} - 5 \setminus \sqrt{5}$.
In general, $\setminus \frac{a}{\setminus \sqrt{b} + \setminus \sqrt{c}} = \setminus \frac{a \left(\setminus \sqrt{b} - \setminus \sqrt{c}\right)}{b - c}$ when $b$ is not equal to $c$. In the case where $b = c > 0$, then $\setminus \frac{a}{\setminus \sqrt{b} + \setminus \sqrt{c}} = \setminus \frac{a}{2 \setminus \sqrt{b}} = \setminus \frac{a \setminus \sqrt{b}}{2 b}$.