Question

How to solve the above question?​

Answer 1

SOLUTION :

$\sf \frac{3 \sqrt{2} - 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} } + \frac{ \sqrt{12} }{ \sqrt{3} - \sqrt{2} }$

$\sf \implies \: \frac{(3 \sqrt{2} - 2 \sqrt{3})(3 \sqrt{2} - 2 \sqrt{3}) }{(3 \sqrt{2} + 2 \sqrt{3} ) (3 \sqrt{2} - 2 \sqrt{3}) } + \frac{ \sqrt{12} ( \sqrt{3} + \sqrt{2}) }{( \sqrt{3} - \sqrt{2} )( \sqrt{3} + \sqrt{2} ) }$

$\sf \implies \: \frac{ {(3 \sqrt{2} - 2 \sqrt{3}) }^{2} }{ {(3 \sqrt{2}) }^{2} - {(2 \sqrt{3} )}^{2} } + \frac{ \sqrt{12} ( \sqrt{3} + \sqrt{2} )}{ {( \sqrt{3})}^{2} - { (\sqrt{2} )}^{2} }$

$\sf \implies \: \frac{18 + 12 - 12 \sqrt{6} }{6} + \sqrt{36} + \sqrt{24}$

$\sf \implies \: 5 - 12 \sqrt{6} + 6 + \sqrt{24}$

$\sf \implies \:11 - 10 \sqrt{6}$