Упростите выражение:
$\frac{1}{(a - 1)(a - 2)} + \frac{1}{(a - 2)(a - 3)} + \frac{1}{(a - 3)(a - 4)}$.
$\frac{1}{(a - 1)(a - 2)} + \frac{1}{(a - 2)(a - 3)} + \frac{1}{(a - 3)(a - 4)} = \frac{(a - 3)(a - 4) + (a - 1)(a - 4) + (a - 1)(a - 2)}{(a - 1)(a - 2)(a - 3)(a - 4)} = \frac{a^2 - 3a - 4a + 12 + a^2 - a - 4a + 4 + a^2 - a - 2a + 2}{(a - 1)(a - 2)(a - 3)(a - 4)} = \frac{3a^2 - 15a + 18}{(a - 1)(a - 2)(a - 3)(a - 4)} = \frac{3(a^2 - 5a + 6)}{(a - 1)(a^2 - 2a - 3a + 6)(a - 4)} = \frac{3(a^2 - 5a + 6)}{(a - 1)(a^2 - 5a + 6)(a - 4)} = \frac{3}{(a - 1)(a - 4)}$
Пожауйста, оцените решение
