Решение:

а) $$\begin{aligned} \frac{\sqrt{50} - \sqrt{10}}{\sqrt{15} - \sqrt{3}} &= \frac{\sqrt{25 \cdot 2} - \sqrt{10}}{\sqrt{3 \cdot 5} - \sqrt{3}} \\ &= \frac{5\sqrt{2} - \sqrt{10}}{\sqrt{3}(\sqrt{5} - 1)} \\ &= \frac{\sqrt{2}(5 - \sqrt{5})}{\sqrt{3}(\sqrt{5} - 1)} \\ &= \frac{\sqrt{2}(5 - \sqrt{5})}{\sqrt{3}(\sqrt{5} - 1)} \cdot \frac{(\sqrt{5} + 1)}{(\sqrt{5} + 1)} \\ &= \frac{\sqrt{2}(5 - \sqrt{5})(\sqrt{5} + 1)}{\sqrt{3}(5 - 1)} \\ &= \frac{\sqrt{2}(5\sqrt{5} + 5 - 5 - \sqrt{5})}{\sqrt{3} \cdot 4} \\ &= \frac{\sqrt{2}(4\sqrt{5})}{4\sqrt{3}} \\ &= \frac{\sqrt{2}\sqrt{5}}{\sqrt{3}} \\ &= \frac{\sqrt{10}}{\sqrt{3}} \\ &= \frac{\sqrt{10} \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}} \\ &= \frac{\sqrt{30}}{3} \end{aligned}$$ Ответ: $$\frac{\sqrt{30}}{3}$$ б) $$\begin{aligned} \frac{a - b}{\sqrt{a} - \sqrt{b}} &= \frac{(\sqrt{a})^2 - (\sqrt{b})^2}{\sqrt{a} - \sqrt{b}} \\ &= \frac{(\sqrt{a} - \sqrt{b})(\sqrt{a} + \sqrt{b})}{\sqrt{a} - \sqrt{b}} \\ &= \sqrt{a} + \sqrt{b} \end{aligned}$$ Ответ: $$\sqrt{a} + \sqrt{b}$$