Question

pls answer this question for 100 points​

Answer 1

that's my way and answer please wish.

Answer 2

$here \: we \: used \: rationalising \\ \\ (1) \implies \: \frac{3 \sqrt{2} }{ \sqrt{6} - \sqrt{3} } \\ \\ rationalising \: by \: \sqrt{6} + \sqrt{3} \\ \\ we \: get \\ \\ \implies \: \frac{3 \sqrt{2} ( \sqrt{6} + \sqrt{3} }{6 - 3} \\ \\ \implies \: \sqrt{12} + \sqrt{6} \\ \\ and \: \\ \\ (2) \: \frac{4 \sqrt{2} }{ \sqrt{6} - \sqrt{2} } \\ \\ rationalising \: by \: \sqrt{6} + \sqrt{2} \\ \\ we \: get \\ \\ \implies \: \frac{4 \sqrt{2} ( \sqrt{6} + \sqrt{2} )}{6 - 2} \\ \\ \implies \: \sqrt{12} + 2 \\ \\ \\ now \\ \\ (3) \: \frac{2 \sqrt{3} }{ \sqrt{6} + \sqrt{2} } \\ \\ rationalising \: by \: \sqrt{6} - \sqrt{2} \\ \\ we \: get \\ \\ \implies \: \frac{2 \sqrt{3}( \sqrt{6} - \sqrt{2}) }{6 - 2} \\ \\ \implies \: \frac{3 - \sqrt{3} }{2 \sqrt{2} } \\ \\ \\ now \: by \: (1)(2)(3) \: finally \: we \: get \: \\ \\ \implies \: \sqrt{12} + \sqrt{6} - \sqrt{12} - 2 + \frac{3 - \sqrt{3} }{2 \sqrt{2} } \\ \\ \implies \: \frac{3 \sqrt{3} - 4 \sqrt{2} + 3}{2 \sqrt{2} } \\ \\ \\ it \: is \: your \: answer$.

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