Question

Simplify
please send fast today is my test

Answer 1

this is ur answer ...I hope it helps you..

Answer 2

Hey friend,
Here is the answer you were looking for:
$\frac{ \sqrt{2} }{ \sqrt{6} - \sqrt{2} } - \frac{ \sqrt{3} }{ \sqrt{6} + \sqrt{2} } \\ \\ on \: rationalizing \: the \: denominator \: we \: get \\ \\ = \frac{ \sqrt{2} }{ \sqrt{6} - \sqrt{2} } \times \frac{ \sqrt{6} + \sqrt{2} }{ \sqrt{6} + \sqrt{2} } - \frac{ \sqrt{3} }{ \sqrt{6} + \sqrt{2} } \times \frac{ \sqrt{6} - \sqrt{2} }{ \sqrt{6} - \sqrt{2} } \\ \\ using \: the \: identity \\ (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ = (\frac{ \sqrt{2} \times \sqrt{6} + \sqrt{2} \times \sqrt{2} }{ {( \sqrt{6}) }^{2} - {( \sqrt{2} )}^{2} }) - ( \frac{ \sqrt{3} \times \sqrt{6} - \sqrt{3} \times \sqrt{2} }{ {( \sqrt{6}) }^{2} - {( \sqrt{2} )}^{2} } ) \\ \\ = (\frac{ \sqrt{2} \times \sqrt{2 \times 3} + \sqrt{2 \times 2} }{6 - 2} ) - (\frac{ \sqrt{3} \times \sqrt{2 \times 3} - \sqrt{6} }{6 - 2} ) \\ \\ = ( \frac{ \sqrt{2 \times 2 \times 3} + \sqrt{2 \times 2} }{4} ) - ( \frac{ \sqrt{3 \times 3 \times 2} - \sqrt{6} }{4} ) \\ \\ = ( \frac{2 \sqrt{3} + 2}{4} ) - ( \frac{3 \sqrt{2} - \sqrt{6} }{4} ) \\ \\ \frac{(2 \sqrt{3} + 2) - (3 \sqrt{2} - \sqrt{6}) }{4} \\ \\ = \frac{2 \sqrt{3} + 2 - 3 \sqrt{2} + \sqrt{6} }{4} \\ \\ = \frac{2 - 3 \sqrt{2} + 2 \sqrt{3} + \sqrt{6} }{4}$

Hope this helps!!!!

@Mahak24

Thanks...
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