6. Сократите дробь: 6+ √6 √30+ √5

6. Сократите дробь:

$$\frac{6 + \sqrt{6}}{\sqrt{30} + \sqrt{5}} = \frac{6 + \sqrt{6}}{\sqrt{5} \cdot \sqrt{6} + \sqrt{5}} = \frac{6 + \sqrt{6}}{\sqrt{5}(\sqrt{6} + 1)} = \frac{\sqrt{6}(\sqrt{6} + 1)}{\sqrt{5}(\sqrt{6} + 1)} = \frac{\sqrt{6}}{\sqrt{5}}$$

$$\frac{\sqrt{6}}{\sqrt{5}} = \frac{\sqrt{6}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = \frac{\sqrt{30}}{5}$$

Ответ: $$\frac{\sqrt{30}}{5}$$