Question

$( \sqrt2 / \sqrt6 - \sqrt2 ) - ( \sqrt3 / \sqrt6 + \sqrt2)$

Answer 1

$\frac{ \sqrt{2} }{ \sqrt{6} - \sqrt{2} } - \frac{ \sqrt{3} }{ \sqrt{6} + \sqrt{2} }$

$= \frac{ \sqrt{2} }{ \sqrt{6} - \sqrt{2} } \times \frac{ \sqrt{6} + \sqrt{2} }{ \sqrt{6} + \sqrt{2} } - \frac{ \sqrt{3} }{ \sqrt{6} + \sqrt{2} } \times \frac{ \sqrt{6} - \sqrt{2} }{ \sqrt{6} - \sqrt{2} } \\ \\ = \frac{ \sqrt{2}( \sqrt{6} + \sqrt{2} )}{ {( \sqrt{6}) }^{2} - {( \sqrt{2}) }^{2} } - \frac{ \sqrt{3}( \sqrt{6} - \sqrt{2} )}{ {( \sqrt{6}) }^{2} - {( \sqrt{2}) }^{2} } \\ \\ = \frac{12 + 2}{6 - 2} - \frac{18 - 6}{6 - 2} \\ \\ = \frac{14}{4} - \frac{12}{4} \\ \\ = \frac{14 - 12}{4} \\ \\ = \frac{2}{4} \\ \\ = \frac{1}{2}$

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