a)
\frac{3-\sqrt2}{\sqrt2+2}=\frac{(3-\sqrt2)(\sqrt2-2)}{(\sqrt2+2)(\sqrt2-2)}=\frac{3\sqrt2-6-2+2\sqrt2}{2-4}=\frac{5\sqrt2-8}{-2}=\frac{-(8-5\sqrt2)}{-2}=\frac{8-5\sqrt2}{2}
b)
\frac{\sqrt3+4}{2\sqrt3+2}=\frac{\sqrt3+4}{2(\\sqrt3+1)}=\frac{(\sqrt3+4)((\sqrt3-1)}{2(\sqrt3+1)(\sqrt3-1)}=\frac{3-\sqrt3+4\sqrt3-4}{2(3-1)}=\frac{3\sqrt3-1}{2*2}=\frac{3\sqrt3-1}{4}