\[\frac{m - 4^{\backslash m + 1}}{m} - \frac{m - 3^{\backslash m}}{m + 1} =\]
\[= \frac{m^{2} - 4m + m - 4 - m^{2} + 3m}{m(m + 1)} =\]
\[= - \frac{4}{m(m + 1)}.\]