Question

simplify:

$\frac{18\sqrt{3}}{12-6\sqrt{2}}+\frac{3\sqrt{2}-2\sqrt{3}}{8-\sqrt{6}}-\frac{12\sqrt{2}+4\sqrt{6}}{8-\sqrt{12}}$

Answer 1

$\frac{18\sqrt{3}}{12-6\sqrt{2}}=\frac{18\sqrt{3}(12-6\sqrt{2})}{(12-6\sqrt{2})(12+6\sqrt{2})}=\frac{18\sqrt{3}(12-6\sqrt{2})}{144-72}\frac{3\sqrt{2}-2\sqrt{2}}{8-\sqrt{6}}=\frac{(3\sqrt{2}-2\sqrt{2})(8-\sqrt{6})}{64-6}=\frac{24\sqrt{2}+6\sqrt{3}-16\sqrt{3}-6\sqrt{2}}{58}\frac{12\sqrt{2}+4\sqrt{6}}{8+\sqrt{12}}=\frac{(12\sqrt{2}+4\sqrt{6})(8+\sqrt{12})}{64-12}=\frac{96\sqrt{2}+24\sqrt{6}+32\sqrt{6}+24\sqrt{2}}{52}$