\[\frac{1^{\backslash a + 1}}{a - 1} - \frac{1^{\backslash a - 1}}{a + 1} =\]
\[= \frac{a + 1 - (a - 1)}{(a - 1)(a + 1)} =\]
\[= \frac{a + 1 - a + 1}{a^{2} - 1} = \frac{2}{a^{2} - 1}\]