Найдите значение выражения: (11/18-17/24):(-5/18+4/15).

Ответ:

\[\left( \frac{11}{18} - \frac{17}{24} \right)\ :\left( - \frac{5}{18} + \frac{4}{15} \right) =\]

\[= \left( \frac{44}{72} - \frac{51}{72} \right)\ :\left( - \frac{25}{90} + \frac{24}{90} \right) =\]

\[= - \left( \frac{51}{72} - \frac{44}{72} \right)\ :\left( - \frac{1}{90} \right) =\]

\[= - \frac{7}{72}\ :\left( - \frac{1}{90} \right) = \frac{7 \cdot 90}{72 \cdot 1} =\]

\[= \frac{35}{4} = 8\frac{3}{4}\]