6. Сократите дробь: 5-√5 √10-√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: $$\frac{\sqrt{10}}{2}$$