\[\frac{5^{\backslash x - 7}}{x + 7} - \frac{3^{\backslash x + 7}}{x - 7} = 0\]
\[\frac{5 \cdot (x - 7) - 3 \cdot (x + 7)}{(x + 7)(x - 7)} = 0;\ \ \ \ \ \ \ \]
\[x \neq 7;\ \ \ x \neq - 7\]
\[5x - 35 - 3x - 21 = 0\]
\[2x - 56 = 0\]
\[2x = 56\]
\[x = 28.\]
\[Ответ:x = 28.\]