1: \(\left[\dfrac{1}{3}\left(\dfrac{6}{5}-\dfrac{9}{4}\right)-\dfrac{7}{5}\left(\dfrac{15}{14}+\dfrac{5}{7}\right)\right]:\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{5}{6}\right)\)
\(=\left[\dfrac{1}{3}\left(\dfrac{24}{20}-\dfrac{45}{20}\right)-\dfrac{7}{5}\left(\dfrac{15}{14}+\dfrac{10}{14}\right)\right]:\left(\dfrac{1}{6}+\dfrac{5}{6}\right)\)
\(=\dfrac{1}{3}\cdot\dfrac{-21}{20}-\dfrac{7}{5}\cdot\dfrac{25}{14}\)
\(=\dfrac{-7}{20}-\dfrac{5}{2}=-\dfrac{7}{20}-\dfrac{50}{20}=-\dfrac{57}{20}\)
2: \(\dfrac{1}{5}:\dfrac{3}{10}+\dfrac{5}{6}\left(\dfrac{12}{5}-\dfrac{6}{25}+\dfrac{18}{75}\right)-\dfrac{18}{17}:\dfrac{9}{34}\)
\(=\dfrac{1}{5}\cdot\dfrac{10}{3}+\dfrac{5}{6}\left(\dfrac{12}{5}-\dfrac{6}{25}+\dfrac{6}{25}\right)-\dfrac{18}{17}\cdot\dfrac{34}{9}\)
\(=\dfrac{2}{3}+\dfrac{5}{6}\cdot\dfrac{12}{5}-4=\dfrac{2}{3}+2-4=\dfrac{2}{3}-2=-\dfrac{4}{3}\)
3: \(\dfrac{10}{7}:\dfrac{5}{14}-\dfrac{2}{3}\left(\dfrac{9}{4}-\dfrac{15}{8}\right):\left(\dfrac{1}{5}-\dfrac{3}{10}+\dfrac{9}{20}\right)\)
\(=\dfrac{10}{7}\cdot\dfrac{14}{5}-\dfrac{2}{3}\cdot\left(\dfrac{18}{8}-\dfrac{15}{8}\right):\left(\dfrac{4}{20}-\dfrac{6}{20}+\dfrac{9}{20}\right)\)
\(=4-\dfrac{2}{3}\cdot\dfrac{3}{8}:\dfrac{7}{20}=4-\dfrac{1}{4}\cdot\dfrac{20}{7}=4-\dfrac{5}{7}=\dfrac{23}{7}\)
4: \(-\dfrac{3}{4}:\left(\dfrac{1}{4}-\dfrac{5}{8}\right)+\dfrac{3}{8}\left(\dfrac{4}{3}-\dfrac{16}{9}\right)-\dfrac{5}{7}\left(\dfrac{14}{15}-\dfrac{21}{10}\right)\)
\(=-\dfrac{3}{4}:\dfrac{-3}{8}+\dfrac{3}{8}\left(\dfrac{12}{9}-\dfrac{16}{9}\right)-\dfrac{5}{7}\cdot\left(\dfrac{28}{30}-\dfrac{63}{30}\right)\)
\(=2+\dfrac{3}{8}\cdot\dfrac{-4}{9}-\dfrac{5}{7}\cdot\dfrac{-35}{30}=2+\dfrac{-1}{6}+\dfrac{5}{6}\)
\(=2+\dfrac{4}{6}=2+\dfrac{2}{3}=\dfrac{8}{3}\)
5: \(\dfrac{10}{3}:\left(-\dfrac{20}{9}\right)-\dfrac{8}{7}\left(\dfrac{21}{4}-\dfrac{14}{8}\right)-\dfrac{3}{4}\cdot\dfrac{8}{9}+12:\dfrac{24}{7}\)
\(=\dfrac{10}{3}\cdot\dfrac{-9}{20}-\dfrac{8}{7}\cdot\left(\dfrac{21}{4}-\dfrac{7}{4}\right)-\dfrac{2}{3}+\dfrac{7}{2}\)
\(=\dfrac{-3}{2}-\dfrac{8}{7}\cdot\dfrac{14}{4}-\dfrac{4}{6}+\dfrac{21}{6}\)
\(=-\dfrac{9}{6}-4+\dfrac{17}{6}=\dfrac{8}{6}-4=\dfrac{4}{3}-4=-\dfrac{8}{3}\)
