\[\frac{x + 4}{2x - 6} - \frac{x + 1}{x - 3} =\]
\[= \frac{x + 4}{2 \cdot (x - 3)} - \frac{x + 1^{\backslash 2}}{x - 3} =\]
\[= \frac{x + 4 - 2x - 2}{2 \cdot (x - 3)} = \frac{2 - x}{2 \cdot (x - 3)}\]