Решение задачи 12.12.25: Упрощение алгебраического выражения

12.12.25

Горшков Тимур

а)

\[ \frac{2a - 6}{a^2 - 6a + 9} - \frac{12}{a^2 - 9} = \frac{2(a - 3)}{(a - 3)^2} - \frac{12}{(a - 3)(a + 3)} = \] \[ = \frac{2}{a - 3} - \frac{12}{(a - 3)(a + 3)} = \frac{2(a + 3) - 12}{(a - 3)(a + 3)} = \] \[ = \frac{2a + 6 - 12}{(a - 3)(a + 3)} = \frac{2a - 6}{(a - 3)(a + 3)} = \frac{2(a - 3)}{(a - 3)(a + 3)} = \frac{2}{a + 3} \]