User:Satori/proof

$\frac{\sqrt{2}-\sqrt{6}}{4}=\frac{-\sqrt{2-\sqrt{3}}}{2}$

Multiplying by two:

$\frac{\sqrt{2}-\sqrt{6}}{2}=-\sqrt{2-\sqrt{3}}$

Squaring both sides:

$\frac{2-2(\sqrt{2}\sqrt{6})+6}{2^2}=2-\sqrt{3}$

Simplified:

$\frac{8-2\sqrt{12}}{4}=2-\sqrt{3}$

Multiplying by four:

$8-2\sqrt{12}=8-4\sqrt{3}$

Subtracting eight and multiplying by negative one:

$2\sqrt{12}=4\sqrt{3}$

Factoring a two from the right side and representing as the square root of four:

$2\sqrt{12}=2\sqrt{4}\sqrt{3}$

$2\sqrt{12}=2\sqrt{12}$