Question

Simplify Each Of The Following​

Answer 1

Answer:

0

Step-by-step explanation:

$\frac{2 \sqrt{6} }{ \sqrt{2 } + \sqrt{3} } + \frac{6 \sqrt{2} }{ \sqrt{6} + \sqrt{3} } - \frac{8 \sqrt{3} }{ \sqrt{6} + \sqrt{2} } \\ = \frac{2 \sqrt{6} }{ \sqrt{2 } + \sqrt{3} } \times \frac{ \sqrt{2} - \sqrt{3} }{ \sqrt{2} - \sqrt{3} } + \frac{6 \sqrt{2} }{ \sqrt{6} + \sqrt{3} } \times \frac{ \sqrt{6} - \sqrt{3} }{\sqrt{6} - \sqrt{3}} - \frac{8 \sqrt{3} }{ \sqrt{6} + \sqrt{2} } \times \frac{ \sqrt{6} - \sqrt{2} }{ \sqrt{6} - \sqrt{2} } \\ = \frac{2 \sqrt{12} - 2 \sqrt{18} }{( \sqrt{2}) ^{2} - (\sqrt{3}) ^{2} } + \frac{6 \sqrt{12} - 6 \sqrt{6} }{ (\sqrt{6}) ^{2} - (\sqrt{3}) ^{2} } - \frac{8 \sqrt{18} - 8 \sqrt{6} }{( \sqrt{6}) ^{2} - (\sqrt{2}) ^{2} } \\ = \frac{4 \sqrt{3} - 6 \sqrt{2} }{2 - 3} + \frac{12 \sqrt{3} - 6 \sqrt{6} }{6 - 3} - \frac{24 \sqrt{2} - 8 \sqrt{6} }{6 - 2} \\ = \frac{4 \sqrt{3} - 6 \sqrt{2} }{ - 1} + \frac{6(2 \sqrt{3} - \sqrt{6}) }{3} - \frac{8(3 \sqrt{2 } - \sqrt{6}) }{4} \\ = - 4 \sqrt{3} + 6 \sqrt{2} + 2(2 \sqrt{3} - \sqrt{6} ) - 2(3 \sqrt{2} - \sqrt{6} ) \\ = - 4 \sqrt{3} + 6 \sqrt{2} + 4 \sqrt{3} - 2 \sqrt{6} - 6 \sqrt{2} + 2 \sqrt{6} \\ = 0$