Вычислите: \(\dfrac{3{,}75:1\frac{1}{2}+(1{,}5:3\frac{3}{4})\cdot2\frac{1}{2}+(1\frac{1}{7}-\frac{23}{49}):\frac{22}{147}}{2:3\frac{1}{5}+(3\frac{1}{4}:13):\frac{2}{3}-(2\frac{5}{18}-\frac{17}{36})\cdot\frac{18}{65}}\).

Вычислим числитель:

\[3{,}75:1\frac12=\frac{15}{4}:\frac32=\frac52.\]

\[(1{,}5:3\frac34)\cdot2\frac12=\left(\frac32:\frac{15}{4}\right)\cdot\frac52=\frac25\cdot\frac52=1.\]

\[\left(1\frac17-\frac{23}{49}\right):\frac{22}{147}=\left(\frac87-\frac{23}{49}\right):\frac{22}{147}=\frac{33}{49}\cdot\frac{147}{22}=\frac92.\]

\[\text{Числитель}=\frac52+1+\frac92=8.\]

Вычислим знаменатель:

\[2:3\frac15=2:\frac{16}{5}=\frac58.\]

\[(3\frac14:13):\frac23=\left(\frac{13}{4}:13\right):\frac23=\frac14\cdot\frac32=\frac38.\]

\[(2\frac5{18}-\frac{17}{36})\cdot\frac{18}{65}=\left(\frac{41}{18}-\frac{17}{36}\right)\cdot\frac{18}{65}=\frac{65}{36}\cdot\frac{18}{65}=\frac12.\]

\[\text{Знаменатель}=\frac58+\frac38-\frac12=\frac12.\]

\[8:\frac12=16.\]

Ответ: \(16\).