Вычисли: [14 − (49 1/3 : 16 − 14 : 8 1/6) · 7] / [1 17/18 · (1 59/70 + 37/42 + 2 19/30) − 10].

Числитель:

\[49\frac13:\,16=\frac{148}{3}:16=\frac{37}{12},\qquad 14:8\frac16=14:\frac{49}{6}=\frac{12}{7}.\]

\[\frac{37}{12}-\frac{12}{7}=\frac{115}{84},\qquad 14-\frac{115}{84}\cdot7=14-\frac{115}{12}=\frac{53}{12}.\]

Знаменатель:

\[1\frac{59}{70}+\frac{37}{42}+2\frac{19}{30}=\frac{129}{70}+\frac{37}{42}+\frac{79}{30}=\frac{1061}{315}.\]

\[1\frac{17}{18}\cdot\frac{1061}{315}-10=\frac{35}{18}\cdot\frac{1061}{315}-10=\frac{1061}{162}-10=-\frac{559}{162}.\]

Тогда

\[\frac{53}{12}:\left(-\frac{559}{162}\right)=\frac{53}{12}\cdot\frac{162}{-559}=-\frac{1431}{559}.\]

Ответ: \(-\frac{1431}{559}\).