4. Упростите выражение: 1) a/a²-10a+25 + a+2/25-a²;

1) $$\frac{a}{a^2 - 10a + 25} + \frac{a+2}{25 - a^2} = \frac{a}{(a-5)^2} - \frac{a+2}{(a-5)(a+5)} = \frac{a(a+5) - (a+2)(a-5)}{(a-5)^2(a+5)} = \frac{a^2 + 5a - (a^2 - 5a + 2a - 10)}{(a-5)^2(a+5)} = \frac{a^2 + 5a - a^2 + 3a + 10}{(a-5)^2(a+5)} = \frac{8a + 10}{(a-5)^2(a+5)} = \frac{2(4a+5)}{(a-5)^2(a+5)}$$

Ответ: $$\frac{2(4a+5)}{(a-5)^2(a+5)}$$