Вычислить: \(\dfrac{(9\frac{1}{4}-4\frac{2}{5})\cdot2\frac{1}{2}-1\frac{1}{2}}{(3\frac{1}{8}+4\frac{3}{20}-1\frac{5}{48}-5\frac{2}{5})\cdot3\frac{1}{12}}+\dfrac{6-4\frac{1}{10}}{7+1:\frac{3}{7}}\).

Вычислим первую дробь:

\[(9\frac{1}{4}-4\frac{2}{5})\cdot2\frac{1}{2}-1\frac{1}{2}=\left(\frac{37}{4}-\frac{22}{5}\right)\cdot\frac{5}{2}-\frac{3}{2}=\frac{97}{20}\cdot\frac{5}{2}-\frac{3}{2}=\frac{97}{8}-\frac{12}{8}=\frac{85}{8}.\]

\[3\frac{1}{8}+4\frac{3}{20}-1\frac{5}{48}-5\frac{2}{5}=\frac{25}{8}+\frac{83}{20}-\frac{53}{48}-\frac{27}{5}=\frac{37}{48}.\]

\[(3\frac{1}{8}+4\frac{3}{20}-1\frac{5}{48}-5\frac{2}{5})\cdot3\frac{1}{12}=\frac{37}{48}\cdot\frac{37}{12}=\frac{1369}{576}.\]

\[\frac{\frac{85}{8}}{\frac{1369}{576}}=\frac{85}{8}\cdot\frac{576}{1369}=\frac{6120}{1369}.\]

Вычислим вторую дробь:

\[6-4\frac{1}{10}=\frac{19}{10},\qquad 7+1:\frac{3}{7}=7+\frac{7}{3}=\frac{28}{3}.\]

\[\frac{6-4\frac{1}{10}}{7+1:\frac{3}{7}}=\frac{19}{10}:\frac{28}{3}=\frac{19}{10}\cdot\frac{3}{28}=\frac{57}{280}.\]

Складываем:

\[\frac{6120}{1369}+\frac{57}{280}=\frac{6120\cdot280+57\cdot1369}{1369\cdot280}=\frac{1791633}{383320}.\]

Ответ: \(\frac{1791633}{383320}\).