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[TEX]\frac{1}{\sqrt{2} + \sqrt{3} + 1}[/TEX]

[TEX]= \frac{\sqrt{2} + \sqrt{3} - 1 }{2(2 + \sqrt{6})}[/TEX]

[TEX]= \frac{(\sqrt{2} + \sqrt{3} - 1 )(\sqrt{6} - 2}{4}[/TEX]

[TEX]= \frac{\sqrt{2} - \sqrt{6} + 2}{4}[/TEX]
 
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