6. Сократите дробь: 5-√5/√10-√2

Сократим дробь: $$\frac{5-\sqrt{5}}{\sqrt{10}-\sqrt{2}}$$.

$$\frac{5-\sqrt{5}}{\sqrt{10}-\sqrt{2}} = \frac{\sqrt{5}(\sqrt{5}-1)}{\sqrt{2}(\sqrt{5}-1)} = \frac{\sqrt{5}}{\sqrt{2}} = \frac{\sqrt{5}\cdot\sqrt{2}}{\sqrt{2}\cdot\sqrt{2}} = \frac{\sqrt{10}}{2}$$.

Ответ: √10/2