Operaciones combinadas con fracciones

Realiza las siguientes operaciones con fracciones. Si es posible, simplifica el resultado.

  1. \(\dfrac{1}{2}-\dfrac{8}{3}-(-2)\left(\dfrac{5}{12}-\dfrac{1}{3}\right)-\left(\dfrac{9}{10}\right):\left(\dfrac{3}{10}+\dfrac{1}{5}\right)\) =
  2. \(\dfrac{7}{4}\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{5}{6}\right)-\dfrac{7}{2}-\dfrac{4}{3}-\dfrac{4}{3}:\left(\dfrac{3}{2}-\dfrac{1}{6}-\dfrac{5}{3}\right)\) =
  3. \(\dfrac{5}{3}-2:\dfrac{8}{3}\cdot\dfrac{1}{2}+\left(\dfrac{8}{5}+\dfrac{1}{2}+\dfrac{9}{10}\right)\left(\dfrac{1}{2}-\dfrac{2}{2}\right)+\dfrac{5}{6}\) =
  4. \(\dfrac{7}{6}+\dfrac{7}{12}-\left(\dfrac{1}{6}\right)\left(\dfrac{1}{6}+\dfrac{7}{3}-\dfrac{1}{2}\right)-(-6)\left(\dfrac{3}{8}-\dfrac{3}{4}\right)\) =
  5. \(5-\left(-\dfrac{14}{3}\right)\left(\dfrac{20}{3}-\dfrac{11}{12}-\dfrac{7}{4}\right)+\dfrac{5}{3}\left(\dfrac{2}{3}-\dfrac{8}{3}\right)-\dfrac{2}{3}\) =
  6. \(\dfrac{1}{12}\left(\dfrac{7}{2}-\dfrac{4}{7}-\dfrac{13}{14}\right)-\dfrac{3}{2}+\dfrac{3}{4}-(-2)\left(1-\dfrac{1}{8}-\dfrac{5}{6}\right)\) =
  7. \(\dfrac{3}{2}+\dfrac{1}{4}\left(\dfrac{7}{5}-\dfrac{11}{15}\right)-\left(\dfrac{16}{3}\right)\left(\dfrac{5}{2}-\dfrac{2}{3}+\dfrac{1}{6}\right)+\dfrac{6}{5}\) =
  8. \(\dfrac{3}{4}+(-2)\left(4-\dfrac{9}{2}\right)-\left(\dfrac{2}{3}\right)\left(\dfrac{13}{4}-\dfrac{9}{7}-\dfrac{3}{14}\right)+\dfrac{5}{12}\) =
  9. \(\dfrac{7}{3}\cdot\dfrac{6}{5}\left(\dfrac{3}{2}-4+\dfrac{7}{3}\right)\left(\dfrac{1}{15}+\dfrac{1}{5}\right)\left(-\dfrac{1}{6}\right)(-3)\dfrac{16}{9}\) =
  10. \(-\dfrac{3}{4}-(-2)\left(7-\dfrac{11}{2}+\dfrac{9}{10}\right)-\dfrac{2}{3}-\dfrac{1}{8}\left(\dfrac{3}{4}+\dfrac{27}{28}\right)\) =
  11. \(2\left(\dfrac{7}{2}-\dfrac{7}{6}-\dfrac{9}{4}\right)+\dfrac{7}{4}\left(-\dfrac{4}{3}\right)\left(\dfrac{5}{12}-\dfrac{1}{6}-\dfrac{9}{4}\right)-\dfrac{1}{2}\) =
  12. \(\dfrac{11}{45}+\dfrac{2}{9}\left(\dfrac{9}{10}-3+\dfrac{3}{2}\right)+\dfrac{1}{30}\left(\dfrac{9}{2}+\dfrac{1}{9}-\dfrac{11}{18}\right)+\dfrac{2}{9}\) =
  13. \(\dfrac{2}{3}-\dfrac{2}{3}\left(\dfrac{25}{2}-\dfrac{7}{3}-\dfrac{13}{6}\right)\left(\dfrac{1}{3}\right)\left(\dfrac{11}{4}-\dfrac{17}{5}-\dfrac{5}{6}\right)-\dfrac{7}{2}\) =
  14. \(\dfrac{5}{6}-\dfrac{1}{2}\left(\dfrac{8}{3}-\dfrac{2}{5}+\dfrac{5}{6}\right)-\dfrac{3}{2}-\left(-\dfrac{11}{8}\right)\left(\dfrac{1}{6}+\dfrac{9}{4}-\dfrac{11}{12}\right)\) =
  15. \(\dfrac{26}{3}\left(\dfrac{3}{5}-\dfrac{2}{5}-\dfrac{1}{10}\right)+\dfrac{7}{6}-\dfrac{5}{12}\left(\dfrac{2}{9}-\dfrac{2}{3}+\dfrac{5}{6}\right)-\dfrac{1}{12}\) =
  16. \(\dfrac{1}{12}+\dfrac{1}{4}+\dfrac{2}{3}-\left(\dfrac{2}{5}\right)-\left(\dfrac{3}{14}-\dfrac{3}{28}-\dfrac{10}{7}\right)\left(\dfrac{7}{2}-5\right)\) =
  1. \(\dfrac{1-2 \cdot \dfrac{1}{6}}{\dfrac{3}{7}-2\cdot \dfrac{1}{2}}-(-4)\left(\dfrac{1}{14}-\dfrac{1}{63}\right)-\dfrac{1}{18}\) =
  2. \(\dfrac{4}{3}-\left(-\dfrac{1}{4}\right)\left(-1-\dfrac{7}{3}\right)-\dfrac{\dfrac{14}{3}\cdot\dfrac{1}{2}-\dfrac{5}{6}}{\dfrac{7}{2}\cdot\dfrac{5}{6}-\dfrac{8}{3}\cdot\dfrac{1}{2}}\) =
  3. \(4\left(\dfrac{4}{3}-\dfrac{3}{2}\right)-\dfrac{\dfrac{11}{24}\cdot 2-\dfrac{5}{6}}{\dfrac{1}{21}+\dfrac{9}{7}-\dfrac{1}{2}:\dfrac{3}{10}}-\dfrac{7}{12}\) =
  4. \(-\dfrac{1}{2}\left(4-\dfrac{5}{2}+\dfrac{7}{6}\right)+\dfrac{\dfrac{1}{6}\cdot\dfrac{46}{11}-\dfrac{4}{11}}{\dfrac{5}{2}-\dfrac{1}{2}\cdot 2-\dfrac{5}{6}}-\dfrac{1}{6}\) =
  5. \(\dfrac{\dfrac{8}{5}-\dfrac{4}{15}-\dfrac{1}{6}\cdot 4}{\dfrac{11}{114}+\dfrac{13}{57}-\dfrac{7}{12}: \dfrac{1}{2}}+6:\left(6-\dfrac{2}{3}\right)-\dfrac{5}{6}\) =
  6. \(-\dfrac{1}{4}:\left(1-\dfrac{7}{6}+\dfrac{1}{3}\right)-\dfrac{1-2 \cdot \dfrac{1}{6}}{4+\dfrac{1}{4}:\dfrac{3}{2}-\dfrac{9}{2}}-\dfrac{3}{4}\) =
  7. \(\dfrac{1}{2}:\left(\dfrac{39}{56}-\dfrac{5}{8}-\dfrac{3}{7}\right)-\dfrac{\dfrac{8}{3}\cdot 3-\dfrac{7}{2}-\dfrac{9}{4}}{-2:\dfrac{4}{3}-1}+\dfrac{7}{4}\) =
  8. \(\dfrac{1}{6}\left(\dfrac{13}{14}-\dfrac{3}{7}-\dfrac{9}{2}\right)+\dfrac{\dfrac{3}{8}\cdot \dfrac{2}{5}-\dfrac{1}{60}\cdot \dfrac{3}{2}}{\dfrac{4}{5}-\dfrac{3}{10}-2}+\dfrac{1}{4}\) =
  9. \(\dfrac{1}{4}+\left(-\dfrac{1}{2}\right):\left(1-\dfrac{5}{3}-\dfrac{1}{12}\right)+\dfrac{\dfrac{11}{12}+\dfrac{7}{4}-\dfrac{1}{6}\cdot 4}{\dfrac{9}{11}-6\cdot \dfrac{1}{2}}\) =
  10. \(\dfrac{-\dfrac{3}{2}-\dfrac{1}{3}:\dfrac{22}{15}-\dfrac{3}{11}}{\dfrac{4}{3}-\dfrac{9}{4}:\dfrac{1}{2}- \dfrac{1}{6}}-\left(-\dfrac{69}{20}\right)\left(\dfrac{3}{2}-\dfrac{4}{3}\right)-\dfrac{3}{8}\) =
  11. \(\dfrac{9}{14}+\left(-\dfrac{1}{3}\right):\left(\dfrac{8}{33}-\dfrac{10}{11}\right)-\dfrac{\dfrac{5}{7}-\dfrac{5}{3}:\dfrac{2}{3}+\dfrac{1}{14}}{\dfrac{5}{4}:\dfrac{3}{2}+\dfrac{8}{3}-\dfrac{3}{2}}\) =
  12. \(\dfrac{\dfrac{7}{4}:\dfrac{3}{2}-\dfrac{21}{2}\cdot\dfrac{1}{3}+\dfrac{1}{3}}{\dfrac{4}{5}-\dfrac{1}{4}-\dfrac{3}{20}}+\dfrac{9}{2}+\left(-\dfrac{1}{6}\right):\left(2-\dfrac{8}{3}\right)\) =
Soluciones