Question

Solve:—
$x = \frac{3 \sqrt{2} }{ \sqrt{6} - \sqrt{3} } - \frac{4 \sqrt{3} }{ \sqrt{6} - \sqrt{2} } - \frac{ 6}{ \sqrt{8} - \sqrt{12} }$
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Answer 1

${\huge{\underbrace{\overbrace{\color{aqua} {Question}}}}}$

$Solve:—</p><p>x = \frac{3 \sqrt{2} }{ \sqrt{6} - \sqrt{3} } - \frac{4 \sqrt{3} }{ \sqrt{6} - \sqrt{2} } - \frac{ 6}{ \sqrt{8} - \sqrt{12} }$

$\huge \color{pink}{Answer:—}$

$⇒\frac{3 \sqrt{2} }{ \sqrt{6} - \sqrt{3} } \times \frac{ \sqrt{6} + \sqrt{3} }{ \sqrt{6} + \sqrt{3} } \\ \\ = \frac{ \cancel6 \sqrt{3} + \cancel3 \sqrt{6} }{ \cancel3} \\ \\ = 2 \sqrt{3} + \sqrt{6}$

$⇒ \frac{4 \sqrt{3} }{ \sqrt{6} - \sqrt{2} } \times \frac{ \sqrt{6} + \sqrt{2} }{ \sqrt{6} + \sqrt{2} } \\ \\ = \frac{ \cancel{12} \sqrt{2 } + \cancel4 \sqrt{6} }{ \cancel4} \\ \\ = 3 \sqrt{2} + \sqrt{6}$

$⇒ \frac{6}{ \sqrt{8} - \sqrt{12} } \times \frac{ \sqrt{8} + \sqrt{12} }{ \sqrt{8} + \sqrt{12} } \\ \\ = - 3 \sqrt{2} - 3 \sqrt{3} \\ \\ = -[3 \sqrt{2} + 3 \sqrt{3}]$

$⇒ \frac{3 \sqrt{2} }{ \sqrt{6} - \sqrt{3} } - \frac{4 \sqrt{3} }{ \sqrt{6} - \sqrt{2} } - \frac{6}{ \sqrt{8} - \sqrt{2} }$

$⇒2 \sqrt{3} + \cancel{\sqrt{6} } - \cancel{3 \sqrt{2}} - \cancel{ \sqrt{6}} + \cancel{3 \sqrt{2} }+ 3 \sqrt{3}$

$⇒2 \sqrt{3} + 3 \sqrt{3}$

$⇒5 \sqrt{3}$

Answer 2

Hope this answer helps you