\[\frac{1^{\backslash x + 2}}{x - 2} - \frac{1^{x - 2}}{x + 2} =\]
\[= \frac{x + 2 - (x - 2)}{(x - 2)(x + 2)} =\]
\[= \frac{x + 2 - x + 2}{x^{2} - 4} = \frac{4}{x^{2} - 4}\]