\[\frac{x + 6^{\backslash x - 1}}{x + 1} - \frac{x - 6^{\backslash x + 1}}{x - 1} =\]
\[- \frac{x^{2} + 6x - x - 6 - x^{2} + 6x - x + 6}{(x - 1)(x + 1)} =\]
\[= \frac{10x}{x^{2} - 1}.\]