Вычислить: б) \(\dfrac{\frac35\cdot\frac5{21}+\frac{15}{28}:\frac5{84}}{5:\frac12+10}+\dfrac{2:\frac12+3:\frac13}{\frac12:2+\frac13:3}\cdot\frac1{36}-1\frac{16}{35}\); в) \(\dfrac{8:\left(3:\left(2\frac34-1\frac{15}{28}\right)+\frac23:\frac32\right)+\frac{57}{223}}{14\cdot\left(5\frac57-4\frac34\right)-9\frac57+\frac3{13}}\).

б) Вычислим первую дробь:

\[\frac35\cdot\frac5{21}=\frac1{7},\qquad \frac{15}{28}:\frac5{84}=9,\qquad 5:\frac12+10=10+10=20.\]

\[\frac{\frac17+9}{20}=\frac{\frac{64}{7}}{20}=\frac{16}{35}.\]

Вторая дробь:

\[2:\frac12+3:\frac13=4+9=13,\qquad \frac12:2+\frac13:3=\frac14+\frac19=\frac{13}{36}.\]

\[\frac{13}{\frac{13}{36}}\cdot\frac1{36}=1.\]

Тогда

\[\frac{16}{35}+1-1\frac{16}{35}=0.\]

Ответ: \(0\).

в) Упростим выражение в числителе:

\[2\frac34-1\frac{15}{28}=\frac{11}{4}-\frac{43}{28}=\frac{77-43}{28}=\frac{34}{28}=\frac{17}{14}.\]

\[3:\frac{17}{14}=\frac{42}{17},\qquad \frac23:\frac32=\frac49.\]

\[\frac{42}{17}+\frac49=\frac{378+68}{153}=\frac{446}{153}.\]

\[8:\frac{446}{153}=8\cdot\frac{153}{446}=\frac{612}{223},\qquad \frac{612}{223}+\frac{57}{223}=\frac{669}{223}=3.\]

Знаменатель:

\[5\frac57-4\frac34=\frac{40}{7}-\frac{19}{4}=\frac{160-133}{28}=\frac{27}{28},\]

\[14\cdot\frac{27}{28}=\frac{27}{2},\qquad 9\frac57=\frac{68}{7}.\]

\[\frac{27}{2}-\frac{68}{7}+\frac3{13}=\frac{2457-1904+42}{182}=\frac{595}{182}=\frac{85}{26}.\]

Следовательно,

\[3:\frac{85}{26}=3\cdot\frac{26}{85}=\frac{78}{85}.\]

Ответ: \(\frac{78}{85}\).