Решите уравнение 6/(x^2-36)-3/(x^2-6x)+(x-12)/(x^2+6x)=0.

Ответ:

\[\frac{6}{x^{2} - 36} - \frac{3}{x^{2} - 6x} + \frac{x - 12}{x^{2} + 6x} = 0\]

\[\frac{6}{(x - 6)(x + 6)} - \frac{3}{x(x - 6)} + \frac{x - 12}{x(x + 6)} = 0\]

\[ОДЗ:\ \ \ x \neq 0;\ \ x \neq 6;\ \ \ x \neq - 6.\]

\[Умножим\ на\ x(x - 6)(x + 6):\]

\[6x - 3 \cdot (x + 6) + (x - 12)(x - 6) = 0\]

\[6x - 3x - 18 + x^{2} - 6x - 12x + 72 = 0\]

\[x^{2} - 15x + 54 = 0\]

\[x_{1} + x_{2} = 15;\ \ x_{1} \cdot x_{2} = 54\]

\[x_{1} = 9;\ \ \ \ \ \ \ \ \ \ \ \ \ \ x_{2} = 6\ (не\ подходит).\]

\[Ответ:x = 9.\]