№5. Упростите выражение: $$(\frac{6}{x^2 - 9} + \frac{1}{3 - x}) \cdot \frac{x^2 + 6x + 9}{5}$$.

$$\left(\frac{6}{x^2 - 9} + \frac{1}{3 - x}\right) \cdot \frac{x^2 + 6x + 9}{5} = \left(\frac{6}{(x - 3)(x + 3)} - \frac{1}{x - 3}\right) \cdot \frac{(x + 3)^2}{5} = \frac{6 - (x + 3)}{(x - 3)(x + 3)} \cdot \frac{(x + 3)^2}{5} = \frac{3 - x}{(x - 3)(x + 3)} \cdot \frac{(x + 3)^2}{5} = -\frac{x - 3}{(x - 3)(x + 3)} \cdot \frac{(x + 3)^2}{5} = -\frac{1}{x + 3} \cdot \frac{(x + 3)^2}{5} = -\frac{x + 3}{5}$$ Ответ: $$\frac{-(x + 3)}{5}$$