Question

simplify 1/(√2+√3-√5)-1/√2-√3+√5​

Answer 1

$\frac{1}{ \sqrt{2} + \sqrt{3} - \sqrt{5} } - \frac{1}{ \sqrt{2} - \sqrt{3} + \sqrt{5} } \\ \\ = > \frac{1}{ \sqrt{2} + ( \sqrt{3} - \sqrt{5}) } - \frac{1}{ \sqrt{2} - ( \sqrt{3} - \sqrt{5}) } \\ \\ = > \frac{ \sqrt{2} - \sqrt{3} + \sqrt{5} + \sqrt{2} + \sqrt{3} - \sqrt{5} }{ (\sqrt{2} +( \sqrt{3 } - \sqrt{5})( \sqrt{2} - ( \sqrt{3} - \sqrt{5}) } \\ \\ = > \frac{2 \sqrt{2} }{2 - {( \sqrt{3} - \sqrt{5}) }^{2} } \\ \\ = > \frac{2 \sqrt{2} }{2 - (3 - 2 \sqrt{15} + 5) } \\ \\ = > \frac{2 \sqrt{2} }{2 - 8 + 2 \sqrt{15} } = \frac{2 \sqrt{2} }{2 \sqrt{15} - 6} \\ \\ = > \frac{2 \sqrt{2} }{2( \sqrt{15} - 3)} = \frac{ \sqrt{2} }{ \sqrt{15} - 3 }$

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