Упростите выражение:
$\frac{1}{(a - 1)(a - 3)} + \frac{1}{(a - 3)(a - 5)} + \frac{1}{(a - 5)(a - 7)}$.
$\frac{1}{(a - 1)(a - 3)} + \frac{1}{(a - 3)(a - 5)} + \frac{1}{(a - 5)(a - 7)} = \frac{(a - 5)(a - 7) + (a - 1)(a - 7) + (a - 1)(a - 3)}{(a - 1)(a - 3)(a - 5)(a - 7)} = \frac{a^2 - 5a - 7a + 35 + a^2 - a - 7a + 7 + a^2 - a - 3a + 3}{(a - 1)(a - 3)(a - 5)(a - 7)} = \frac{3a^2 - 24a + 45}{(a - 1)(a - 3)(a - 5)(a - 7)} = \frac{3(a^2 - 8a + 15)}{(a - 1)(a^2 - 3a - 5a + 15)(a - 7)} = \frac{3(a^2 - 8a + 15)}{(a - 1)(a^2 - 8a + 15)(a - 7)} = \frac{3}{(a - 1)(a - 7)}$
Пожауйста, оцените решение
