\[\frac{x + 2}{2x - 4} - \frac{3x - 2}{x^{2} - 2x} =\]
\[= \frac{x + 2}{2 \cdot (x - 2)} - \frac{3x - 2}{x(x - 2)} =\]
\[= \frac{x^{2} + 2x - 6x + 4}{2x(x - 2)} =\]
\[= \frac{x - 2}{2x}\ \]