7. Найдите значение выражения $$\left(9a^2 - \frac{9}{16b^2}\right) : \left(3a - \frac{3}{4b}\right)$$ при $$a = \frac{2}{3}$$ и $$b = -\frac{1}{12}$$.

Решение: \begin{aligned} &\left(9a^2 - \frac{9}{16b^2}\right) : \left(3a - \frac{3}{4b}\right) = \frac{9a^2 - \frac{9}{16b^2}}{3a - \frac{3}{4b}} = \frac{9\left(a^2 - \frac{1}{16b^2}\right)}{3\left(a - \frac{1}{4b}\right)} = \frac{3\left(a - \frac{1}{4b}\right)\left(a + \frac{1}{4b}\right)}{a - \frac{1}{4b}} = 3\left(a + \frac{1}{4b}\right)\\ &\text{Подставим значения } a = \frac{2}{3}, b = -\frac{1}{12}:\
&3\left(\frac{2}{3} + \frac{1}{4\left(-\frac{1}{12}\right)}\right) = 3\left(\frac{2}{3} + \frac{1}{-\frac{1}{3}}\right) = 3\left(\frac{2}{3} - 3\right) = 3\left(\frac{2}{3} - \frac{9}{3}\right) = 3\left(-\frac{7}{3}\right) = -7 \end{aligned} **Ответ: -7**