Решите уравнение: 1/(x^2-6x)+1/(x^2+6x)=2x/(x^2-36).

Ответ:

\[\frac{1}{x² - 6x} + \frac{1}{x² + 6x} = \frac{2x}{x² - 36}\]

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

\[= \frac{2x^{\backslash x}}{(x - 6)(x + 6)},\ \ \]

\[x \neq 0,\ x \neq 6,\ x \neq - 6\]

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

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

\[2x(1 - x) = 0\]

\[x = 0 \Longrightarrow не\ подходит.\]

\[x = 1.\]

\[Ответ:x = 1.\]