2. Найдите значение выражения \((\frac{7}{u} + \frac{7}{6v}) : \frac{u+6v}{u^2}\) при \(u = \sqrt{192}, v = \sqrt{3}\).

1. Упростим выражение:

$$\left(\frac{7}{u} + \frac{7}{6v}\right) : \frac{u+6v}{u^2} = \frac{7(6v+u)}{6uv} : \frac{u+6v}{u^2} = \frac{7(u+6v)}{6uv} \cdot \frac{u^2}{u+6v} = \frac{7u^2}{6uv} = \frac{7u}{6v}$$

2. Подставим значения \(u = \sqrt{192}, v = \sqrt{3}\):

$$\frac{7u}{6v} = \frac{7\sqrt{192}}{6\sqrt{3}} = \frac{7\sqrt{64 \cdot 3}}{6\sqrt{3}} = \frac{7 \cdot 8 \sqrt{3}}{6\sqrt{3}} = \frac{7 \cdot 8}{6} = \frac{56}{6} = \frac{28}{3} = 9\frac{1}{3}$$

Ответ: \(9\frac{1}{3}\)