Вычислите: \(\left(\left(1\frac{1}{7}-\frac{23}{49}\right):\frac{22}{147}-\left(0{,}6:3\frac{3}{4}\right)\right)2\frac{1}{2}+3{,}75:1\frac{1}{2}\right):2{,}2\).

\[1\frac{1}{7}-\frac{23}{49}=\frac{8}{7}-\frac{23}{49}=\frac{56-23}{49}=\frac{33}{49}.\]

\[\frac{33}{49}:\frac{22}{147}=\frac{33}{49}\cdot\frac{147}{22}=\frac{33\cdot3}{22}=\frac{9}{2}.\]

\[0{,}6:3\frac{3}{4}=\frac{3}{5}:\frac{15}{4}=\frac{3}{5}\cdot\frac{4}{15}=\frac{4}{25}.\]

\[\frac{9}{2}-\frac{4}{25}=\frac{225-8}{50}=\frac{217}{50}.\]

\[\frac{217}{50}\cdot2\frac{1}{2}+3{,}75:1\frac{1}{2}=\frac{217}{50}\cdot\frac{5}{2}+\frac{15}{4}:\frac{3}{2}=\frac{217}{20}+\frac{5}{2}=\frac{267}{20}.\]

\[\frac{267}{20}:2{,}2=\frac{267}{20}:\frac{11}{5}=\frac{267}{20}\cdot\frac{5}{11}=\frac{267}{44}.\]

Ответ: \(\frac{267}{44}=6\frac{3}{44}\).