\[\frac{3m + 2}{m - 3} - 2^{\backslash m - 3} =\]
\[= \frac{3m + 2 - 2 \cdot (m - 3)}{m - 3} =\]
\[= \frac{3m + 2 - 2m + 6}{m - 3} = \frac{m + 8}{m - 3}\]