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Question Number 22174 by Adoy last updated on 12/Oct/17

Answered by $@ty@m last updated on 13/Oct/17

$$$$$$=\frac{4-5\sqrt{3}}{2+\sqrt{6}}$$$$=\frac{4-5\sqrt{3}}{2+\sqrt{6}}\times \frac{2-\sqrt{6}}{2-\sqrt{6}}$$$$=\frac{(4-5\sqrt{}3)(2-\sqrt{6})}{(2+\sqrt{6})(2-\sqrt{6)}}$$$$=\frac{8-4\sqrt{}6-10\sqrt{3}+5\sqrt{18}}{2^2-\sqrt{6^2}}$$$$=\frac{8-4\sqrt{}6-10\sqrt{3}+5\sqrt{18}}{-2}$$$$=-4+2\sqrt{6}+5\sqrt{3}-\frac{5}{2}\sqrt{18}$$

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