Ta có : 

• $\frac{3}{\sqrt{3}+1}=\frac{3(\sqrt{3}-1)}{3-1}=\frac{3(\sqrt{3}-1)}{2}$
• $\frac{2}{\sqrt{3}-1}=\frac{2(\sqrt{3}+1)}{3-1}=\sqrt{3}+1$
• $\frac{2+\sqrt{3}}{2-\sqrt{3}}=\frac{(2+\sqrt{3})^{2}}{2^{2}-3}=(2+\sqrt{3})^{2}=7+4\sqrt{3}$
• $\frac{b}{3+\sqrt{b}}=\frac{b(3-\sqrt{b})}{9-b}$
• $\frac{p}{2\sqrt{p}-1}=\frac{p(2\sqrt{p}+1)}{(2\sqrt{p})^{2}-1^{2}}=\frac{2p\sqrt{p}+p}{4p-1}$