Упростите выражение:
$\frac{1}{a(a + 3)} + \frac{1}{(a + 3)(a + 6)} + \frac{1}{(a + 6)(a + 9)} + \frac{1}{(a + 9)(a + 12)}$.
$\frac{1}{a(a + 3)} + \frac{1}{(a + 3)(a + 6)} + \frac{1}{(a + 6)(a + 9)} + \frac{1}{(a + 9)(a + 12)} = (\frac{1}{a(a + 3)} + \frac{1}{(a + 3)(a + 6)}) + (\frac{1}{(a + 6)(a + 9)} + \frac{1}{(a + 9)(a + 12)}) = \frac{(a + 6) + a}{a(a + 3)(a + 6)} + \frac{(a + 12) + (a + 6)}{(a + 6)(a + 9)(a + 12)} = \frac{a + 6 + a}{a(a + 3)(a + 6)} + \frac{a + 12 + a + 6}{(a + 6)(a + 9)(a + 12)} = \frac{2a + 6}{a(a + 3)(a + 6)} + \frac{2a + 18}{(a + 6)(a + 9)(a + 12)} = \frac{2(a + 3)}{a(a + 3)(a + 6)} + \frac{2(a + 9)}{(a + 6)(a + 9)(a + 12)} = \frac{2}{a(a + 6)} + \frac{2}{(a + 6)(a + 12)} = \frac{2(a + 12) + 2a}{a(a + 6)(a + 12)} = \frac{2a + 24 + 2a}{a(a + 6)(a + 12)} = \frac{4a + 24}{a(a + 6)(a + 12)} = \frac{4(a + 6)}{a(a + 6)(a + 12)} = \frac{4}{a(a + 12)}$
Пожауйста, оцените решение
