6. Найдите значение выражения: а) \(2\frac{2}{3}:1\frac{7}{9}+\frac{55}{84}:\left(\frac{43}{63}-\frac{23}{36}\right)\); б) \(5\frac{5}{7}:\frac{8}{21}+1\frac{8}{13}\cdot\left(\frac{43}{56}-\frac{11}{24}\right)\).

а)

\[2\frac23:1\frac79=\frac83:\frac{16}{9}=\frac32.\]

\[\frac{43}{63}-\frac{23}{36}=\frac{172}{252}-\frac{161}{252}=\frac{11}{252}.\]

\[\frac{55}{84}:\frac{11}{252}=\frac{55}{84}\cdot\frac{252}{11}=15.\]

\[\frac32+15=\frac{33}{2}=16\frac12.\]

б)

\[5\frac57:\frac8{21}=\frac{40}{7}\cdot\frac{21}{8}=15.\]

\[\frac{43}{56}-\frac{11}{24}=\frac{129}{168}-\frac{77}{168}=\frac{13}{42}.\]

\[1\frac8{13}\cdot\frac{13}{42}=\frac{21}{13}\cdot\frac{13}{42}=\frac12.\]

\[15+\frac12=\frac{31}{2}=15\frac12.\]

Ответ: а) \(16\frac12\); б) \(15\frac12\).