[tex]\frac{2}{\sqrt{5}-1} =\frac{2}{\sqrt{5}-1} *\frac{ \sqrt{5}+1}{\sqrt{5}+1} = \frac{2(\sqrt{5}+1)}{5-1}= \frac{\not{2}^1 *(\sqrt{5}+1)}{\not{4})^2}=\frac{\sqrt{5}+1}{2}[/tex]
[tex]\frac{4\sqrt{3}}{2+\sqrt{6}} = \frac{4\sqrt{3}}{2+\sqrt{6}}*\frac{2-\sqrt{6}}{2-\sqrt{6}}=\frac{4 \sqrt{3}(2-\sqrt{6}) }{4-6}=\frac{\not{4}^2 \sqrt{3}(2-\sqrt{6}) }{-\not{2}^1}=\\\\=-2\sqrt{3}(2-\sqrt{6})=-4\sqrt{3}+2\sqrt{18}=-4\sqrt{3}+2\sqrt{9*2}=-4\sqrt{3}+2*3\sqrt{2}=\\\\=6\sqrt{2}-4\sqrt{3}[/tex]
