Решите уравнение: 10/(x^2-100)+(x-20)/(x^2-10x)-5/(x^2-10x)=0.

\[\frac{10^{\backslash x}}{x^{2} - 100} + \frac{x - 20^{\backslash x + 10}}{x^{2} - 10x} - \frac{5^{\backslash x - 10}}{x^{2} + 10x} = 0\]

\[ОДЗ:x \neq 0;x \neq \pm 10.\]

\[\frac{10x + x^{2} - 20x + 10x - 200 - 5x + 50}{x(x - 10)(x + 10)} = 0\]

\[x^{2} - 5x - 150 = 0\]

\[x_{1} + x_{2} = 5;\ \ x_{1} \cdot x_{2} = - 150\]

\[x_{1} = 15;\ \ x_{2} = - 10\ (не\ подходит)\]

\[Ответ:x = 15.\]