\(\dfrac{5}{6}:\left(-\dfrac{10}{9}\right)+-\dfrac{3}{4}.\dfrac{8}{9}+12:\dfrac{24}{7}\left(\dfrac{5}{6}-\dfrac{4}{3}+\dfrac{1}{2}\right)\)
\(=-\dfrac{3}{4}-\dfrac{2}{3}+12:\dfrac{24}{7}\left(\dfrac{5}{6}-\dfrac{8}{6}+\dfrac{3}{6}\right)\)
\(=-\dfrac{9}{12}-\dfrac{8}{12}+12:\dfrac{24}{7}.0\)
\(=-\dfrac{17}{12}\)
\(\dfrac{5}{6}:\left(\dfrac{10}{-9}\right)+\dfrac{-3}{4}\cdot\dfrac{8}{9}+12:\dfrac{24}{7}\cdot\left(\dfrac{5}{6}-\dfrac{4}{3}+\dfrac{1}{2}\right)\)
\(=-\dfrac{3}{4}+\dfrac{-2}{3}+0=-\dfrac{17}{12}\)