Решить уравнение: (x-2)/(x+2)=(x+3)/(x-4).

\[\frac{x - 2}{x + 2} = \frac{x + 3}{x - 4}\]

\[x \neq - 2;\ \ x \neq 4.\]

\[(x - 2)(x - 4) = (x + 2)(x + 3)\]

\[x^{2} - 2x - 4x + 8 = x^{2} + 2x + 3x + 6\]

\[- 6x - 5x = 6 - 8\]

\[- 11x = - 2\]

\[x = \frac{2}{11}.\]