$\frac{6}{x - 2} - \frac{x + 3}{x} = \frac{x + 6}{x^2 - 2x}$
x − 2 ≠ 0
x ≠ 2
x ≠ 0
$\frac{6}{x - 2} - \frac{x + 3}{x} = \frac{x + 6}{x^2 - 2x}$
$\frac{6x - (x + 3)(x - 2)}{x(x - 2)} = \frac{x + 6}{x(x - 2)} |* x(x - 2)$
$6x - (x^2 + 3x - 2x - 6) = x + 6$
$6x - (x^2 + x - 6) = x + 6$
$6x - x^2 - x + 6 - x - 6 = 0$
$4x - x^2 = 0$
x(4 − x) = 0
x = 0 − не подходит
или
4 − x = 0
x = 4
Ответ: x = 4