a)
\frac{\sqrt6}{2-2\sqrt3}=\frac{\sqrt6*(2+2\sqrt3)}{(2-2\sqrt3)*(2+2\sqrt3)}=\frac{2\sqrt6+2\sqrt{18}}{4-4*3}=\frac{2\sqrt6+2\sqrt{9*2}}{4-12}=\frac{2\sqrt6+6\sqrt2}{-8}=\frac{2(\sqrt6+3\sqrt2)}{-8}=-\frac{\sqrt6+3\sqrt2}{4}
b)
\frac{1+\sqrt2}{3+\sqrt2}=\frac{(1+\sqrt2)*(3-\sqrt2)}{(3+\sqrt2)*(3-\sqrt2)}=\frac{3-\sqrt2+3\sqrt2-2}{9-2}=\frac{1+2\sqrt2}{7}