$\frac{3}{5x + 25} + \frac{1}{2x - 10} = \frac{5}{x^2 - 25}$
$\frac{3}{5(x + 5)} + \frac{1}{2(x - 5)} = \frac{5}{(x - 5)(x + 5)}$
$\frac{3 * 2(x - 5) + 5(x + 5)}{10(x - 5)(x + 5)} = \frac{5}{(x - 5)(x + 5)}$
$\frac{6(x - 5) + 5(x + 5)}{10(x - 5)(x + 5)} = \frac{5 * 10}{10(x - 5)(x + 5)}$
$\frac{6x - 30 + 5x + 25}{10(x - 5)(x + 5)} = \frac{50}{10(x - 5)(x + 5)}$
10(x − 5)(x + 5) ≠ 0
(x − 5)(x + 5) ≠ 0
x − 5 ≠ 0
x ≠ 5
и
x + 5 ≠ 0
x ≠ −5
6x − 30 + 5x + 25 = 50
11x − 5 = 50
11x = 50 + 5
11x = 55
x = 5 − не является корнем уравнения
Ответ: нет корней