Упростите выражение $$1 + \frac{5a - 1}{a^2 - 10a + 25} - \frac{a}{a - 5}$$.

$$1 + \frac{5a - 1}{a^2 - 10a + 25} - \frac{a}{a - 5} = 1 + \frac{5a - 1}{(a - 5)^2} - \frac{a}{a - 5} = \frac{(a - 5)^2 + (5a - 1) - a(a - 5)}{(a - 5)^2} = \frac{a^2 - 10a + 25 + 5a - 1 - a^2 + 5a}{(a - 5)^2} = \frac{24}{(a - 5)^2}$$