$\frac{x + 2}{x^2 - 2x + 1} * \frac{3x - 3}{x^2 - 4} - \frac{3}{x - 2} = \frac{x + 2}{(x - 1)^2} * \frac{3(x - 1)}{(x - 2)(x + 2)} - \frac{3}{x - 2} = \frac{3}{(x - 1)(x - 2)} - \frac{3}{x - 2} = \frac{3}{x - 2}(\frac{1}{x - 1} - 1) = \frac{3}{x - 2} * \frac{1 - (x - 1)}{x - 1} = \frac{3(2 - x)}{(x - 2)(x - 1)} = -\frac{3}{x - 1} = \frac{3}{1 - x}$

$\frac{a - 2}{4a^2 + 16a + 16} : (\frac{a}{2a - 4} - \frac{a^2 + 4}{2a^2 - 8} - \frac{2}{a^2 + 2a}) = \frac{a - 2}{4(a^2 + 4a + 4)} : (\frac{a}{2(a - 2)} - \frac{a^2 + 4}{2(a^2 - 4)} - \frac{2}{a(a + 2)}) = \frac{a - 2}{4(a + 2)^2} : (\frac{a^2(a + 2) - a(a^2 + 4) - 2 * 2(a - 2)}{2a(a - 2)(a + 2)}) = \frac{a - 2}{4(a + 2)^2} * \frac{2a(a - 2)(a + 2)}{a^3 + 2a^2 - a^3 - 4a - 4a + 8} = \frac{a(a - 2)^2}{2(a + 2)(2a^2 - 8a + 8)} = \frac{a(a - 2)^2}{4(a + 2)(a^2 - 4a + 4)} = \frac{a(a - 2)^2}{4(a + 2)(a - 2)^2} = \frac{a}{4(a + 2)}$