\[\frac{x - 3^{\backslash x - 3}}{x - 4} > \frac{x - 4^{\backslash x - 4}}{x - 3}\]
\[\frac{(x - 3)^{2} - (x - 4)^{2}}{(x - 3)(x - 4)} > 0\]
\[\frac{x^{2} - 6x + 9 - x^{2} + 8x - 16}{(x - 3)(x - 4)} < 0\]
\[\frac{2x - 7}{(x - 3)(x - 4)} < 0\]
\[\frac{2 \cdot (x - 3,5)}{(x - 3)(x - 4)} > 0\]
\[Ответ:(3;3,5) \cup (4; + \infty)\text{.\ }\]