Решение:

1. $$\frac{\sqrt{35} - \sqrt{15}}{\sqrt{14} - \sqrt{6}} = \frac{\sqrt{5}(\sqrt{7} - \sqrt{3})}{\sqrt{2}(\sqrt{7} - \sqrt{3})} = \frac{\sqrt{5}}{\sqrt{2}} = \frac{\sqrt{5} \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} = \frac{\sqrt{10}}{2}$$
2. $$\frac{\sqrt{a} - \sqrt{b}}{a - b} = \frac{\sqrt{a} - \sqrt{b}}{(\sqrt{a} - \sqrt{b})(\sqrt{a} + \sqrt{b})} = \frac{1}{\sqrt{a} + \sqrt{b}}$$
3. $$\frac{x - 2\sqrt{xy} + y}{x - y} = \frac{(\sqrt{x} - \sqrt{y})^2}{(\sqrt{x} - \sqrt{y})(\sqrt{x} + \sqrt{y})} = \frac{\sqrt{x} - \sqrt{y}}{\sqrt{x} + \sqrt{y}}$$
4. $$\frac{a-9}{\sqrt{a}+3} = \frac{(\sqrt{a} - 3)(\sqrt{a} + 3)}{\sqrt{a} + 3} = \sqrt{a} - 3$$