\[\boxed{\mathbf{1044}\mathbf{.}\mathbf{\ }}\]
\[1)\ \frac{1}{2 \cdot 3} = \frac{a^{\backslash 3}}{2} - \frac{b^{\backslash 2}}{3}\]
\[\frac{1}{6} = \frac{3a - 2b}{6}\]
\[3a - 2b = 1\]
\[a = b = 1.\]
\[2)\ \frac{4}{3 \cdot 5} = \frac{a}{3} - \frac{b}{5}\]
\[\frac{4}{15} = \frac{5a - 3b}{15}\]
\[5a - 3b = 4\]
\[a = b = 2.\]