\[\frac{x - 2^{\backslash x - 2}}{x - 3} > \frac{x - 3^{\backslash x - 3}}{x - 2}\]
\[\frac{(x - 2)^{2} - (x - 3)^{2}}{(x - 2)(x - 3)} > 0\]
\[\frac{x^{2} - 4x + 4 - x^{2} + 6x - 9}{(x - 2)(x - 3)} > 0\]
\[\frac{2x - 5}{(x - 2)(x - 3)} > 0\]
\[\frac{2 \cdot (x - 2,5)}{(x - 2)(x - 3)} > 0\]
\[Ответ:(2;2,5) \cup (3; + \infty).\]