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

Ответ:

\[\frac{100}{x² - 100} + \frac{x - 20}{x² + 10x} - \frac{5}{x^{2} - 10x} = 0\]

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

\[ОДЗ:\ \ x \neq 0;\ \ \ \ \ x \neq 10;\ \ \ \ \ x \neq - 10.\]

\[Умножим\ на\ x(x - 10)(x + 10):\]

\[10x + (x - 20)(x - 10) - 5 \cdot (x + 10) = 0\]

\[10x + x² - 10x - 20x + 200 - 5x - 50 = 0\]

\[x² - 25x + 150 = 0\]

\[x_{1} + x_{2} = 25;\ \ \ \ x_{1} \cdot x_{2} = 150\]

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

\[Ответ:x = 15.\]