a) $$rac{2}{\sqrt{2}} = \frac{2 \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} = \frac{2\sqrt{2}}{2} = \sqrt{2}$$
b) $$rac{4}{2\sqrt{2}} = \frac{2}{\sqrt{2}} = \sqrt{2}$$
c) $$rac{4}{3\sqrt{2}} = \frac{4\sqrt{2}}{3\sqrt{2}\sqrt{2}} = \frac{4\sqrt{2}}{3 \cdot 2} = \frac{4\sqrt{2}}{6} = \frac{2\sqrt{2}}{3}$$
d) $$rac{1}{\sqrt{2}\sqrt{2}} = \frac{1}{2}$$