Решите уравнение x/(x+5)-25/(x^2+5x)=0.

Ответ:

\[\frac{x}{x + 5} - \frac{25}{x^{2} + 5x} = 0\]

\[\frac{x}{x + 5} - \frac{25}{x(x + 5)} = 0\ \ \ \ \ \ \ | \cdot x(x + 5)\text{\ \ }\]

\[ОДЗ:\ x \neq 0,\ x \neq 5\]

\[x^{2} - 25 = 0\]

\[(x - 5)(x + 5) = 0\]

\[x - 5 = 0\ \ \ \ \ \ \ \ \ x + 5 = 0\]

\[x = 5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - 5\ (не\ подходит)\]

\[Ответ:x = 5.\]