Question

3 root2➖2 root 3 / 3 root2 ➕ 2 root3 +root 12 /root 3 ➖ root2

Answer 1

$(2 \sqrt{6} + 18 - \sqrt{2} ) \div ( \sqrt{3} )$

Answer 2

$\frac{3 \sqrt{2} - 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} } + \frac{2 \sqrt{3} + \sqrt{12} }{ \sqrt{3} - \sqrt{2} } \\ = \frac{(3 \sqrt{2} - 2 \sqrt{3} )(3 \sqrt{2} - 2 \sqrt{3} )}{(3 \sqrt{2} + 2 \sqrt{3} )(3 \sqrt{2} - 2 \sqrt{3} )} + \frac{(2 \sqrt{3} + 2 \sqrt{3}) ( \sqrt{3} + \sqrt{2} ) }{( \sqrt{3} + \sqrt{2} )( \sqrt{3} - \sqrt{2} )} \\ = \frac{ {(3 \sqrt{2} )}^{2} + {(2 \sqrt{3} )}^{2} - 2 \times 3 \sqrt{2} \times 2 \sqrt{3} }{ {(3 \sqrt{2} )}^{2} - {(2 \sqrt{3} )}^{2} } + \frac{4 \sqrt{6}( \sqrt{3} + \sqrt{2}) }{3 - 2} \\ = \frac{18 + 12 - 12 \sqrt{6} }{18 - 12} + 12 \sqrt{2} + 8 \sqrt{3 } \\ = 3 + 2 + 2 \sqrt{6} + 12 \sqrt{2} + 8 \sqrt{3} \\ = 5 + 12 \sqrt{2} + 8 \sqrt{3} + 2 \sqrt{6}$
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