5. Сократите дробь: a) $$\frac{5 - \sqrt{10}}{\sqrt{10} - 2}$$; б) $$\frac{25 - b}{\sqrt{b} + 5}$$

Решение:

a) $$\frac{5 - \sqrt{10}}{\sqrt{10} - 2} = \frac{-\sqrt{5}(\sqrt{2} - \sqrt{5})}{\sqrt{2}(\sqrt{5} - \sqrt{2})} = \frac{-\sqrt{5}(\sqrt{2} - \sqrt{5})}{\sqrt{2}(\sqrt{5} - \sqrt{2})} = -\frac{\sqrt{5}}{\sqrt{2}} = -\frac{\sqrt{10}}{2}$$

б) $$\frac{25 - b}{\sqrt{b} + 5} = \frac{(5 - \sqrt{b})(5 + \sqrt{b})}{\sqrt{b} + 5} = 5 - \sqrt{b}$$

Ответ: а) $$-\frac{\sqrt{10}}{2}$$, б) $$5 - \sqrt{b}$$