# How do you simplify sqrt2 / (2 sqrt6-sqrt2)?

$\frac{\sqrt{2}}{2 \sqrt{6} - \sqrt{2}} = \frac{\sqrt{2} \left(2 \sqrt{6} + \sqrt{2}\right)}{\left(2 \sqrt{6} - \sqrt{2}\right) \left(2 \sqrt{6} + \sqrt{2}\right)} = \frac{2 \sqrt{2} \sqrt{6} + 2}{24 - 2} = \frac{2 \sqrt{12} + 2}{22} = \frac{\sqrt{2}}{11} + \frac{1}{11}$