Решить уравнение: x^2/(x+3)-x/(x-2)=(x-12)/(x-2)(x+3).

Ответ:

\[\frac{{x^{2}}^{\backslash x - 2}}{x + 3} - \frac{x^{\backslash x + 3}}{x - 2} = \frac{x - 12}{(x - 2)(x + 3)}\]

\[\frac{x^{3} - 2x^{2} - x^{2} - 3x - x + 12}{(x - 2)(x + 3)} = 0\]

\[\frac{x^{3} - 3x^{2} - 4x + 12}{(x - 2)(x + 3)} = 0\]

\[\frac{x^{2}(x - 3) - 4(x - 3)}{(x - 2)(x + 3)} = 0\]

\[ОДЗ:x \neq 2;x \neq - 3.\]

\[(x - 3)\left( x^{2} - 4 \right) = 0\]

\[1)\ x - 3 = 0\]

\[x = 3.\]

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

\[x^{2} = 4\]

\[x = 2\ (не\ подходит);\]

\[x = - 2.\]

\[Ответ:x = - 2;x = 3.\]