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1/root5+root3-root2

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$\frac{1}{\sqrt{5} + (\sqrt{3} - \sqrt{2})} = \frac{1}{\sqrt{5} + (\sqrt{3} - \sqrt{2})} \times \frac{\sqrt{5} - (\sqrt{3} - \sqrt{2})}{\sqrt{5} - (\sqrt{3} - \sqrt{2})} = \frac{\sqrt{5} - \sqrt{3} + \sqrt{2}}{{\sqrt{5}}^{2} - {(\sqrt{3} - \sqrt{2})}^{2}} = \frac{\sqrt{5} - \sqrt{3} + \sqrt{2}}{5 - (3 + 2 - 2 \sqrt{6})} = \frac{\sqrt{5} - \sqrt{3} + \sqrt{2}}{5 - (5 - 2 \sqrt{6})} = \frac{\sqrt{5} - \sqrt{3} + \sqrt{2}}{5 - 5 + 2 \sqrt{6}} = \frac{\sqrt{5} - \sqrt{3} + \sqrt{2}}{2 \sqrt{6}} = \frac{\sqrt{5} - \sqrt{3} + \sqrt{2}}{2 \sqrt{6}} \times \frac{\sqrt{6}}{\sqrt{6}} = \frac{\sqrt{30} - \sqrt{18} + \sqrt{12}}{12} = \frac{\sqrt{30}}{12} - \frac{\sqrt{18}}{12} + \frac{\sqrt{12}}{12} = \frac{\sqrt{30}}{12} - \frac{3 \sqrt{2}}{12} + \frac{2 \sqrt{3}}{12} = \frac{\sqrt{30} - 3 \sqrt{2} + 2 \sqrt{3}}{12}$

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