Question

Find the simplified value.
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Answer 1

$= \frac{1}{ \sqrt{2} + \sqrt{3} - \sqrt{5} } + \frac{1}{ \sqrt{2} - \sqrt{3} - \sqrt{5} } \\ = \frac{ \sqrt{2 } - \sqrt{3} - \sqrt{5} + \sqrt{2} + \sqrt{3} - \sqrt{5} }{ ( \sqrt{2} + \sqrt{3} - \sqrt{5} )( \sqrt{2} - \sqrt{3} - \sqrt{5} )} \\ = \frac{2 \sqrt{2} - 2 \sqrt{5} }{2 - \sqrt{6} - \sqrt{10} + \sqrt{6} - 3 - \sqrt{15} - \sqrt{10} + \sqrt{15} - 5 } \\ = \frac{2( \sqrt{2} - \sqrt{5} )}{2 - 3 - 5} \\ = \frac{2( \sqrt{2} - \sqrt{5} )}{ - 6}$