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