Решите уравнение 4/(x^2-10x+25)-10/(x^2-25 )=1/(x+5).

Ответ:

\[\frac{4}{x^{2} - 10x + 25} - \frac{10}{x^{2} - 25\ } = \frac{1}{x + 5}\]

\[\frac{4}{(x - 5)^{2}} - \frac{10}{(x - 5)(x + 5)} - \frac{1}{x + 5} = 0\]

\[ОДЗ:\ \ \ x \neq 5;\ \ x \neq - 5.\]

\[4 \cdot (x + 5) - 10 \cdot (x - 5) - (x - 5)^{2} = 0\]

\[4x + 20 - 10x + 50 - x^{2} + 10x - 25 = 0\]

\[- x^{2} + 4x + 45 = 0\]

\[x^{2} - 4x - 45 = 0\]

\[x_{1} + x_{2} = 4;\ \ x_{1} \cdot x_{2} = - 45\]

\[x_{1} = 9;\ \ \ \ \ x_{2} = - 5\ (не\ подходит).\]

\[Ответ:x = 9.\]