Ta có :

• $\frac{2+\sqrt{2}}{1+\sqrt{2}}=\frac{\sqrt{2}(\sqrt{2}+1)}{1+\sqrt{2}}=\sqrt{2}$
• $\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}=\frac{\sqrt{5}(\sqrt{3}-1)}{1-\sqrt{3}}=-\sqrt{5}$ 
• $\frac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}=\frac{\sqrt{2}.\sqrt{2}.\sqrt{3}-\sqrt{6}}{\sqrt{4.2}-2}=\frac{\sqrt{6}(\sqrt{2}-1)}{2(\sqrt{2}-1)}=\frac{\sqrt{6}}{2}$
• $\frac{a-\sqrt{a}}{1-\sqrt{a}}=\frac{\sqrt{a}(\sqrt{a}-1)}{1-\sqrt{a}}=-\sqrt{a}$
• $\frac{p-2\sqrt{p}}{\sqrt{p}-2}=\frac{\sqrt{p}(\sqrt{p}-2)}{\sqrt{p}-2}=\sqrt{p}$