Question Number 22174 by Adoy last updated on 12/Oct/17
Answered by $@ty@m last updated on 13/Oct/17
$$ \\ $$$$=\frac{\mathrm{4}−\mathrm{5}\sqrt{\mathrm{3}}}{\mathrm{2}+\sqrt{\mathrm{6}}} \\ $$$$=\frac{\mathrm{4}−\mathrm{5}\sqrt{\mathrm{3}}}{\mathrm{2}+\sqrt{\mathrm{6}}}×\frac{\mathrm{2}−\sqrt{\mathrm{6}}}{\mathrm{2}−\sqrt{\mathrm{6}}} \\ $$$$=\frac{\left(\mathrm{4}−\mathrm{5}\sqrt{}\mathrm{3}\right)\left(\mathrm{2}−\sqrt{\mathrm{6}}\right)}{\left(\mathrm{2}+\sqrt{\mathrm{6}}\right)\left(\mathrm{2}−\sqrt{\left.\mathrm{6}\right)}\right.} \\ $$$$=\frac{\mathrm{8}−\mathrm{4}\sqrt{}\mathrm{6}−\mathrm{10}\sqrt{\mathrm{3}}+\mathrm{5}\sqrt{\mathrm{18}}}{\mathrm{2}^{\mathrm{2}} −\sqrt{\mathrm{6}^{\mathrm{2}} }} \\ $$$$=\frac{\mathrm{8}−\mathrm{4}\sqrt{}\mathrm{6}−\mathrm{10}\sqrt{\mathrm{3}}+\mathrm{5}\sqrt{\mathrm{18}}}{−\mathrm{2}} \\ $$$$=−\mathrm{4}+\mathrm{2}\sqrt{\mathrm{6}}+\mathrm{5}\sqrt{\mathrm{3}}−\frac{\mathrm{5}}{\mathrm{2}}\sqrt{\mathrm{18}} \\ $$