Simplify $\frac{1}{\sqrt{4+2\sqrt{3}} - \sqrt{4-2\sqrt{3}}}$ Simplify $$\frac{1}{\sqrt{4+2\sqrt{3}} - \sqrt{4-2\sqrt{3}}}$$
I know there is another easier method except the one I answered. I cannot find it. Can you please help? Thanks in advance.

My attempt
$$\frac{1}{\sqrt{4+2\sqrt{3}} - \sqrt{4-2\sqrt{3}}}$$
$$ =\frac{\sqrt{4+2\sqrt{3}} + \sqrt{4-2\sqrt{3}}}{4+2\sqrt{3} - (4-2\sqrt{3})} $$
$$ =\frac{\sqrt{4+2\sqrt{3}} + \sqrt{4-2\sqrt{3}}}{4\sqrt{3}} $$
$$ = \sqrt{\left(\frac{\sqrt{4+2\sqrt{3}} + \sqrt{4-2\sqrt{3}}}{4\sqrt{3}} \right)^2}$$
$$ = \sqrt{\frac{4 + 2\sqrt{3} - (4 - 2\sqrt{3}) - 2\sqrt{4^2 - 4\times3}}{48}}$$
$$ = \sqrt{\frac{4 + 2\sqrt{3} + (4 - 2\sqrt{3}) + 2\sqrt{4^2 - 4\times3}}{48}}$$
$$ = \sqrt{\frac{12}{48}} = \sqrt{\frac{1}{4}}$$
$$\mathbf{= \frac{1}{2}}$$
