\[\frac{2x^{\backslash x + 2}}{x - 2} - \frac{x^{\backslash x - 2}}{x + 2} = \frac{2x^{2} + 4x - x^{2} + 2x}{(x - 2)(x + 2)} =\]
\[= \frac{x^{2} + 6x}{x^{2} - 4}\]