Question

please answer me fast

Answer 1

3√2/√3(√2-1) -4√3/√2(√3-1) +2√3/√2(√3+1)
√6/(√2-1) +{(-√6/√3-1) +√6(√3+1)}
√6/(√2-1)+{-3√2-√6+3√2-√6/3-1
√6/(√2-1)+2√6/2
√6+2√3-√6/(√2-1)
2√3/(√2-1) ×√2+1/√2+1
2√6+2√3/2-1
2√3(√2+1)
is your answer

Answer 2

Heya !!!

$\frac{3 \sqrt{2} }{ \sqrt{6} - \sqrt{3} } - \frac{4 \sqrt{3} }{ \sqrt{6} - \sqrt{2} } + \frac{2 \sqrt{3} }{ \sqrt{6} + \sqrt{2} }$

On rationalizing the denominator we get,

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

Hope this helps ☺