Решите уравнение: 6/(x^2-2x)-12/(x^2+2x)=1/x.

\[\frac{6}{x^{2} - 2x} - \frac{12}{x^{2} + 2x} = \frac{1}{x}\]

\[\frac{6^{\backslash x + 2}}{x(x - 2)} - \frac{12^{\backslash x - 2}}{x(x + 2)} = \frac{1^{\backslash(x^{2} - 4)}}{x}\text{\ \ }\]

\[x \neq 0;\ \ x \neq \pm 2;\]

\[6x + 12 - 12x + 24 = x^{2} - 4\]

\[x^{2} + 6x - 40 = 0\]

\[D_{1} = 9 + 40 = 49\]

\[x_{1} = - 3 + 7 = 4;\ \]

\[x_{2} = - 3 - 7 = - 10.\]

\[Ответ:x = - 10;\ x = 4.\]