\frac{2}{\sqrt{5}}=\frac{2*\sqrt{5}}{\sqrt{5}*\sqrt{5}}=\frac{2\sqrt{5}}{5}
\frac{4-\sqrt{3}}{\sqrt{3}}=\frac{(4-\sqrt{3})*\sqrt{3}}{\sqrt{3}*\sqrt{3}}=\frac{4\sqrt{3}-\sqrt{3}*\sqrt{3}}{\sqrt{3}*\sqrt{3}}=\frac{4\sqrt{3}-3}{3}
\frac{\sqrt{2}}{1-\sqrt{2}}=\frac{\sqrt{2}*(1+\sqrt{2})}{(1-\sqrt{2})*(1+\sqrt{2})}=\frac{\sqrt{2}+\sqrt{2}*\sqrt{2}}{1^2-(\sqrt{2})^2}=\frac{\sqrt{2}+2}{1-2}=-(\sqrt{2}+2)=-2-\sqrt{2}
\frac{1+\sqrt{2}}{\sqrt{2}-1}=\frac{(1+\sqrt{2})(\sqrt{2}+1)}{(\sqrt{2}-1)(\sqrt{2}+1)}=\frac{(1+\sqrt{2})^2}{(\sqrt{2})^2-1^1}=\frac{1+1\sqrt{2}+2}{2-1}=2\sqrt{2}+3