a) \(\dfrac{\sqrt{2}}{1+\sqrt{2}-\sqrt{3}}=\dfrac{\sqrt{2}\left(1+\sqrt{2}+\sqrt{3}\right)}{\left(1+\sqrt{2}-\sqrt{3}\right)\left(1+\sqrt{2}+\sqrt{3}\right)}\dfrac{\sqrt{2}+2+\sqrt{6}}{\left(1+\sqrt{2}\right)^2-3}=\dfrac{\sqrt{2}+2+\sqrt{6}}{2\sqrt{2}+3-3}=\dfrac{\sqrt{2}+2+\sqrt{6}}{2\sqrt{2}}=\dfrac{1+\sqrt{2}+\sqrt{3}}{2}\)
b) \(\dfrac{1}{\sqrt{3}+\sqrt{2}-\sqrt{5}}=\dfrac{\sqrt{3}+\sqrt{2}+\sqrt{5}}{\left(\sqrt{3}+\sqrt{2}-\sqrt{5}\right)\left(\sqrt{3}+\sqrt{2}+\sqrt{5}\right)}=\dfrac{\sqrt{3}+\sqrt{2}+\sqrt{5}}{\left(\sqrt{3}+\sqrt{2}\right)^2-5}=\dfrac{\sqrt{3}+\sqrt{2}+\sqrt{5}}{2\sqrt{6}+5-5}=\dfrac{\sqrt{3}+\sqrt{2}+\sqrt{5}}{2\sqrt{6}}=\dfrac{3\sqrt{2}+2\sqrt{3}+\sqrt{30}}{2\sqrt{6}\cdot\sqrt{6}}=\dfrac{3\sqrt{2}+2\sqrt{3}+\sqrt{30}}{12}\)
