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

Mar 14, 2016

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

Explanation:

Note the difference of squares identity:

${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

We use this with $a = \sqrt{6}$ and $b = \sqrt{5}$ below...

Multiply both numerator and denominator by $\sqrt{6} + \sqrt{5}$ ...

$\frac{2}{\sqrt{6} - \sqrt{5}} = \frac{2}{\sqrt{6} - \sqrt{5}} \cdot \frac{\sqrt{6} + \sqrt{5}}{\sqrt{6} + \sqrt{5}}$

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

$= 2 \left(\sqrt{6} + \sqrt{5}\right)$