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Exercice

L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
Si vous regénérez la page (F5) les valeurs seront changées.
La correction se trouve en bas de page.


Exercice


Calculer \[\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{344}{15}-\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{49}{19}}{7}}{7}}{\dfrac{71}{2}}}{\dfrac{71}{2}}-\dfrac{\dfrac{-20}{7}}{7}-\left(\dfrac{11}{2}-\dfrac{351}{4}-0+\dfrac{349}{3}\right)}{-10}}{-\dfrac{173}{2}}}{\dfrac{149}{8}\times\dfrac{351}{4}\times\dfrac{71}{2}\times\dfrac{\dfrac{\dfrac{\dfrac{-14}{-\dfrac{83}{3}}}{-17}}{-20}}{\dfrac{351}{4}}}-\left(\dfrac{\dfrac{\dfrac{\dfrac{1}{-20}}{\dfrac{\dfrac{\dfrac{-20}{-20}}{\dfrac{113}{10}}}{\dfrac{111}{4}}}}{\dfrac{-\dfrac{83}{3}}{-\dfrac{20}{11}}}}{16}-\left(-10\right)\times\left(-\dfrac{349}{3}\right)\times\dfrac{149}{8}-\dfrac{351}{4}-\dfrac{344}{15}-\dfrac{344}{15}\right)}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{28}{15}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{-17}{-\dfrac{20}{11}}}{\left(-\dfrac{349}{3}\right)\times\left(-20\right)\times\dfrac{113}{10}\times\left(-\dfrac{49}{19}\right)}}{\dfrac{344}{15}}}{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{349}{3}}{\dfrac{28}{15}}}{-\dfrac{49}{19}}}{-\dfrac{49}{19}}}{\dfrac{344}{15}}}}}{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{83}{3}}{\dfrac{113}{10}}}{-10}}{-\dfrac{173}{2}}}{\dfrac{309}{11}}\times\left(\dfrac{149}{8}-20+16+\dfrac{111}{4}-\dfrac{123}{14}\right)\times\dfrac{344}{15}\times\dfrac{309}{11}\times\dfrac{11}{2}\times0}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{28}{15}}{0}}{1-7}}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{344}{15}-\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{49}{19}}{7}}{7}}{\dfrac{71}{2}}}{\dfrac{71}{2}}-\dfrac{\dfrac{-20}{7}}{7}-\left(\dfrac{11}{2}-\dfrac{351}{4}-0+\dfrac{349}{3}\right)}{-10}}{-\dfrac{173}{2}}}{\dfrac{149}{8}\times\dfrac{351}{4}\times\dfrac{71}{2}\times\dfrac{\dfrac{\dfrac{\dfrac{-14}{-\dfrac{83}{3}}}{-17}}{-20}}{\dfrac{351}{4}}}-\left(\dfrac{\dfrac{\dfrac{\dfrac{1}{-20}}{\dfrac{\dfrac{\dfrac{-20}{-20}}{\dfrac{113}{10}}}{\dfrac{111}{4}}}}{\dfrac{-\dfrac{83}{3}}{-\dfrac{20}{11}}}}{16}-\left(-10\right)\times\left(-\dfrac{349}{3}\right)\times\dfrac{149}{8}-\dfrac{351}{4}-\dfrac{344}{15}-\dfrac{344}{15}\right)}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{28}{15}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{-17}{-\dfrac{20}{11}}}{\left(-\dfrac{349}{3}\right)\times\left(-20\right)\times\dfrac{113}{10}\times\left(-\dfrac{49}{19}\right)}}{\dfrac{344}{15}}}{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{349}{3}}{\dfrac{28}{15}}}{-\dfrac{49}{19}}}{-\dfrac{49}{19}}}{\dfrac{344}{15}}}}}{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{83}{3}}{\dfrac{113}{10}}}{-10}}{-\dfrac{173}{2}}}{\dfrac{309}{11}}\times\left(\dfrac{149}{8}-20+16+\dfrac{111}{4}-\dfrac{123}{14}\right)\times\dfrac{344}{15}\times\dfrac{309}{11}\times\dfrac{11}{2}\times0}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{28}{15}}{0}}{1-7}}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}=0\) . Voici le détail : \begin{eqnarray*} X &=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{344}{15}-\dfrac{\dfrac{\dfrac{-\dfrac{7}{19}}{7}}{\dfrac{71}{2}}}{\dfrac{71}{2}}-\dfrac{\dfrac{-20}{7}}{7}-\left(\dfrac{11}{2}-\dfrac{351}{4}-0+\dfrac{349}{3}\right)}{-10}}{-\dfrac{173}{2}}}{\dfrac{149}{8}\times\dfrac{351}{4}\times\dfrac{71}{2}\times\dfrac{\dfrac{\dfrac{\dfrac{-14}{-\dfrac{83}{3}}}{-17}}{-20}}{\dfrac{351}{4}}}-\left(\dfrac{\dfrac{\dfrac{\dfrac{1}{-20}}{\dfrac{\dfrac{\dfrac{-20}{-20}}{\dfrac{113}{10}}}{\dfrac{111}{4}}}}{\dfrac{-\dfrac{83}{3}}{-\dfrac{20}{11}}}}{16}-\left(-10\right)\times\left(-\dfrac{349}{3}\right)\times\dfrac{149}{8}-\dfrac{351}{4}-\dfrac{344}{15}-\dfrac{344}{15}\right)}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{28}{15}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{-17}{-\dfrac{20}{11}}}{\left(-\dfrac{349}{3}\right)\times\left(-20\right)\times\dfrac{113}{10}\times\left(-\dfrac{49}{19}\right)}}{\dfrac{344}{15}}}{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{349}{3}}{\dfrac{28}{15}}}{-\dfrac{49}{19}}}{-\dfrac{49}{19}}}{\dfrac{344}{15}}}}}{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{83}{3}}{\dfrac{113}{10}}}{-10}}{-\dfrac{173}{2}}}{\dfrac{309}{11}}\times\left(\dfrac{149}{8}-20+16+\dfrac{111}{4}-\dfrac{123}{14}\right)\times\dfrac{344}{15}\times\dfrac{309}{11}\times\dfrac{11}{2}\times0}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{28}{15}}{0}}{1-7}}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{344}{15}-\dfrac{\dfrac{-\dfrac{1}{19}}{\dfrac{71}{2}}}{\dfrac{71}{2}}-\dfrac{\dfrac{-20}{7}}{7}-\left(\dfrac{11}{2}-\dfrac{351}{4}-0+\dfrac{349}{3}\right)}{-10}}{-\dfrac{173}{2}}}{\dfrac{149}{8}\times\dfrac{351}{4}\times\dfrac{71}{2}\times\dfrac{\dfrac{\dfrac{\dfrac{-14}{-\dfrac{83}{3}}}{-17}}{-20}}{\dfrac{351}{4}}}-\left(\dfrac{\dfrac{\dfrac{\dfrac{1}{-20}}{\dfrac{\dfrac{\dfrac{-20}{-20}}{\dfrac{113}{10}}}{\dfrac{111}{4}}}}{\dfrac{-\dfrac{83}{3}}{-\dfrac{20}{11}}}}{16}-\left(-10\right)\times\left(-\dfrac{349}{3}\right)\times\dfrac{149}{8}-\dfrac{351}{4}-\dfrac{344}{15}-\dfrac{344}{15}\right)}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{28}{15}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{-17}{-\dfrac{20}{11}}}{\left(-\dfrac{349}{3}\right)\times\left(-20\right)\times\dfrac{113}{10}\times\left(-\dfrac{49}{19}\right)}}{\dfrac{344}{15}}}{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{349}{3}}{\dfrac{28}{15}}}{-\dfrac{49}{19}}}{-\dfrac{49}{19}}}{\dfrac{344}{15}}}}}{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{83}{3}}{\dfrac{113}{10}}}{-10}}{-\dfrac{173}{2}}}{\dfrac{309}{11}}\times\left(\dfrac{149}{8}-20+16+\dfrac{111}{4}-\dfrac{123}{14}\right)\times\dfrac{344}{15}\times\dfrac{309}{11}\times\dfrac{11}{2}\times0}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{28}{15}}{0}}{1-7}}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{344}{15}-\dfrac{-\dfrac{2}{1349}}{\dfrac{71}{2}}-\dfrac{\dfrac{-20}{7}}{7}-\left(\dfrac{11}{2}-\dfrac{351}{4}-0+\dfrac{349}{3}\right)}{-10}}{-\dfrac{173}{2}}}{\dfrac{149}{8}\times\dfrac{351}{4}\times\dfrac{71}{2}\times\dfrac{\dfrac{\dfrac{\dfrac{-14}{-\dfrac{83}{3}}}{-17}}{-20}}{\dfrac{351}{4}}}-\left(\dfrac{\dfrac{\dfrac{\dfrac{1}{-20}}{\dfrac{\dfrac{\dfrac{-20}{-20}}{\dfrac{113}{10}}}{\dfrac{111}{4}}}}{\dfrac{-\dfrac{83}{3}}{-\dfrac{20}{11}}}}{16}-\left(-10\right)\times\left(-\dfrac{349}{3}\right)\times\dfrac{149}{8}-\dfrac{351}{4}-\dfrac{344}{15}-\dfrac{344}{15}\right)}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{28}{15}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{-17}{-\dfrac{20}{11}}}{\left(-\dfrac{349}{3}\right)\times\left(-20\right)\times\dfrac{113}{10}\times\left(-\dfrac{49}{19}\right)}}{\dfrac{344}{15}}}{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{349}{3}}{\dfrac{28}{15}}}{-\dfrac{49}{19}}}{-\dfrac{49}{19}}}{\dfrac{344}{15}}}}}{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{83}{3}}{\dfrac{113}{10}}}{-10}}{-\dfrac{173}{2}}}{\dfrac{309}{11}}\times\left(\dfrac{149}{8}-20+16+\dfrac{111}{4}-\dfrac{123}{14}\right)\times\dfrac{344}{15}\times\dfrac{309}{11}\times\dfrac{11}{2}\times0}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{28}{15}}{0}}{1-7}}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{344}{15}+\dfrac{4}{95779}-\dfrac{\dfrac{-20}{7}}{7}-\left(\dfrac{11}{2}-\dfrac{351}{4}-0+\dfrac{349}{3}\right)}{-10}}{-\dfrac{173}{2}}}{\dfrac{149}{8}\times\dfrac{351}{4}\times\dfrac{71}{2}\times\dfrac{\dfrac{\dfrac{\dfrac{-14}{-\dfrac{83}{3}}}{-17}}{-20}}{\dfrac{351}{4}}}-\left(\dfrac{\dfrac{\dfrac{\dfrac{1}{-20}}{\dfrac{\dfrac{\dfrac{-20}{-20}}{\dfrac{113}{10}}}{\dfrac{111}{4}}}}{\dfrac{-\dfrac{83}{3}}{-\dfrac{20}{11}}}}{16}-\left(-10\right)\times\left(-\dfrac{349}{3}\right)\times\dfrac{149}{8}-\dfrac{351}{4}-\dfrac{344}{15}-\dfrac{344}{15}\right)}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{28}{15}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{-17}{-\dfrac{20}{11}}}{\left(-\dfrac{349}{3}\right)\times\left(-20\right)\times\dfrac{113}{10}\times\left(-\dfrac{49}{19}\right)}}{\dfrac{344}{15}}}{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{349}{3}}{\dfrac{28}{15}}}{-\dfrac{49}{19}}}{-\dfrac{49}{19}}}{\dfrac{344}{15}}}}}{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{83}{3}}{\dfrac{113}{10}}}{-10}}{-\dfrac{173}{2}}}{\dfrac{309}{11}}\times\left(\dfrac{149}{8}-20+16+\dfrac{111}{4}-\dfrac{123}{14}\right)\times\dfrac{344}{15}\times\dfrac{309}{11}\times\dfrac{11}{2}\times0}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{28}{15}}{0}}{1-7}}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{344}{15}+\dfrac{4}{95779}-\dfrac{-\dfrac{20}{7}}{7}-\left(\dfrac{11}{2}-\dfrac{351}{4}-0+\dfrac{349}{3}\right)}{-10}}{-\dfrac{173}{2}}}{\dfrac{149}{8}\times\dfrac{351}{4}\times\dfrac{71}{2}\times\dfrac{\dfrac{\dfrac{\dfrac{-14}{-\dfrac{83}{3}}}{-17}}{-20}}{\dfrac{351}{4}}}-\left(\dfrac{\dfrac{\dfrac{\dfrac{1}{-20}}{\dfrac{\dfrac{\dfrac{-20}{-20}}{\dfrac{113}{10}}}{\dfrac{111}{4}}}}{\dfrac{-\dfrac{83}{3}}{-\dfrac{20}{11}}}}{16}-\left(-10\right)\times\left(-\dfrac{349}{3}\right)\times\dfrac{149}{8}-\dfrac{351}{4}-\dfrac{344}{15}-\dfrac{344}{15}\right)}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{28}{15}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{-17}{-\dfrac{20}{11}}}{\left(-\dfrac{349}{3}\right)\times\left(-20\right)\times\dfrac{113}{10}\times\left(-\dfrac{49}{19}\right)}}{\dfrac{344}{15}}}{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{349}{3}}{\dfrac{28}{15}}}{-\dfrac{49}{19}}}{-\dfrac{49}{19}}}{\dfrac{344}{15}}}}}{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{83}{3}}{\dfrac{113}{10}}}{-10}}{-\dfrac{173}{2}}}{\dfrac{309}{11}}\times\left(\dfrac{149}{8}-20+16+\dfrac{111}{4}-\dfrac{123}{14}\right)\times\dfrac{344}{15}\times\dfrac{309}{11}\times\dfrac{11}{2}\times0}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{28}{15}}{0}}{1-7}}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{344}{15}+\dfrac{4}{95779}+\dfrac{20}{49}-\left(\dfrac{11}{2}-\dfrac{351}{4}-0+\dfrac{349}{3}\right)}{-10}}{-\dfrac{173}{2}}}{\dfrac{149}{8}\times\dfrac{351}{4}\times\dfrac{71}{2}\times\dfrac{\dfrac{\dfrac{\dfrac{-14}{-\dfrac{83}{3}}}{-17}}{-20}}{\dfrac{351}{4}}}-\left(\dfrac{\dfrac{\dfrac{\dfrac{1}{-20}}{\dfrac{\dfrac{\dfrac{-20}{-20}}{\dfrac{113}{10}}}{\dfrac{111}{4}}}}{\dfrac{-\dfrac{83}{3}}{-\dfrac{20}{11}}}}{16}-\left(-10\right)\times\left(-\dfrac{349}{3}\right)\times\dfrac{149}{8}-\dfrac{351}{4}-\dfrac{344}{15}-\dfrac{344}{15}\right)}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{28}{15}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{-17}{-\dfrac{20}{11}}}{\left(-\dfrac{349}{3}\right)\times\left(-20\right)\times\dfrac{113}{10}\times\left(-\dfrac{49}{19}\right)}}{\dfrac{344}{15}}}{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{349}{3}}{\dfrac{28}{15}}}{-\dfrac{49}{19}}}{-\dfrac{49}{19}}}{\dfrac{344}{15}}}}}{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{83}{3}}{\dfrac{113}{10}}}{-10}}{-\dfrac{173}{2}}}{\dfrac{309}{11}}\times\left(\dfrac{149}{8}-20+16+\dfrac{111}{4}-\dfrac{123}{14}\right)\times\dfrac{344}{15}\times\dfrac{309}{11}\times\dfrac{11}{2}\times0}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{28}{15}}{0}}{1-7}}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{344}{15}+\dfrac{4}{95779}+\dfrac{20}{49}-\left(-\dfrac{329}{4}-0+\dfrac{349}{3}\right)}{-10}}{-\dfrac{173}{2}}}{\dfrac{149}{8}\times\dfrac{351}{4}\times\dfrac{71}{2}\times\dfrac{\dfrac{\dfrac{\dfrac{-14}{-\dfrac{83}{3}}}{-17}}{-20}}{\dfrac{351}{4}}}-\left(\dfrac{\dfrac{\dfrac{\dfrac{1}{-20}}{\dfrac{\dfrac{\dfrac{-20}{-20}}{\dfrac{113}{10}}}{\dfrac{111}{4}}}}{\dfrac{-\dfrac{83}{3}}{-\dfrac{20}{11}}}}{16}-\left(-10\right)\times\left(-\dfrac{349}{3}\right)\times\dfrac{149}{8}-\dfrac{351}{4}-\dfrac{344}{15}-\dfrac{344}{15}\right)}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{28}{15}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{-17}{-\dfrac{20}{11}}}{\left(-\dfrac{349}{3}\right)\times\left(-20\right)\times\dfrac{113}{10}\times\left(-\dfrac{49}{19}\right)}}{\dfrac{344}{15}}}{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{349}{3}}{\dfrac{28}{15}}}{-\dfrac{49}{19}}}{-\dfrac{49}{19}}}{\dfrac{344}{15}}}}}{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{83}{3}}{\dfrac{113}{10}}}{-10}}{-\dfrac{173}{2}}}{\dfrac{309}{11}}\times\left(\dfrac{149}{8}-20+16+\dfrac{111}{4}-\dfrac{123}{14}\right)\times\dfrac{344}{15}\times\dfrac{309}{11}\times\dfrac{11}{2}\times0}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{28}{15}}{0}}{1-7}}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{344}{15}+\dfrac{4}{95779}+\dfrac{20}{49}-\left(-\dfrac{329}{4}+\dfrac{349}{3}\right)}{-10}}{-\dfrac{173}{2}}}{\dfrac{149}{8}\times\dfrac{351}{4}\times\dfrac{71}{2}\times\dfrac{\dfrac{\dfrac{\dfrac{-14}{-\dfrac{83}{3}}}{-17}}{-20}}{\dfrac{351}{4}}}-\left(\dfrac{\dfrac{\dfrac{\dfrac{1}{-20}}{\dfrac{\dfrac{\dfrac{-20}{-20}}{\dfrac{113}{10}}}{\dfrac{111}{4}}}}{\dfrac{-\dfrac{83}{3}}{-\dfrac{20}{11}}}}{16}-\left(-10\right)\times\left(-\dfrac{349}{3}\right)\times\dfrac{149}{8}-\dfrac{351}{4}-\dfrac{344}{15}-\dfrac{344}{15}\right)}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{28}{15}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{-17}{-\dfrac{20}{11}}}{\left(-\dfrac{349}{3}\right)\times\left(-20\right)\times\dfrac{113}{10}\times\left(-\dfrac{49}{19}\right)}}{\dfrac{344}{15}}}{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{349}{3}}{\dfrac{28}{15}}}{-\dfrac{49}{19}}}{-\dfrac{49}{19}}}{\dfrac{344}{15}}}}}{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{83}{3}}{\dfrac{113}{10}}}{-10}}{-\dfrac{173}{2}}}{\dfrac{309}{11}}\times\left(\dfrac{149}{8}-20+16+\dfrac{111}{4}-\dfrac{123}{14}\right)\times\dfrac{344}{15}\times\dfrac{309}{11}\times\dfrac{11}{2}\times0}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{28}{15}}{0}}{1-7}}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{344}{15}+\dfrac{4}{95779}+\dfrac{20}{49}-\dfrac{409}{12}}{-10}}{-\dfrac{173}{2}}}{\dfrac{149}{8}\times\dfrac{351}{4}\times\dfrac{71}{2}\times\dfrac{\dfrac{\dfrac{\dfrac{-14}{-\dfrac{83}{3}}}{-17}}{-20}}{\dfrac{351}{4}}}-\left(\dfrac{\dfrac{\dfrac{\dfrac{1}{-20}}{\dfrac{\dfrac{\dfrac{-20}{-20}}{\dfrac{113}{10}}}{\dfrac{111}{4}}}}{\dfrac{-\dfrac{83}{3}}{-\dfrac{20}{11}}}}{16}-\left(-10\right)\times\left(-\dfrac{349}{3}\right)\times\dfrac{149}{8}-\dfrac{351}{4}-\dfrac{344}{15}-\dfrac{344}{15}\right)}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{28}{15}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{-17}{-\dfrac{20}{11}}}{\left(-\dfrac{349}{3}\right)\times\left(-20\right)\times\dfrac{113}{10}\times\left(-\dfrac{49}{19}\right)}}{\dfrac{344}{15}}}{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{349}{3}}{\dfrac{28}{15}}}{-\dfrac{49}{19}}}{-\dfrac{49}{19}}}{\dfrac{344}{15}}}}}{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{83}{3}}{\dfrac{113}{10}}}{-10}}{-\dfrac{173}{2}}}{\dfrac{309}{11}}\times\left(\dfrac{149}{8}-20+16+\dfrac{111}{4}-\dfrac{123}{14}\right)\times\dfrac{344}{15}\times\dfrac{309}{11}\times\dfrac{11}{2}\times0}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{28}{15}}{0}}{1-7}}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{344}{15}+\dfrac{4}{95779}+\dfrac{20}{49}-\dfrac{409}{12}}{-10}}{-\dfrac{173}{2}}}{\dfrac{149}{8}\times\dfrac{351}{4}\times\dfrac{71}{2}\times\dfrac{\dfrac{\dfrac{\dfrac{42}{83}}{-17}}{-20}}{\dfrac{351}{4}}}-\left(\dfrac{\dfrac{\dfrac{\dfrac{1}{-20}}{\dfrac{\dfrac{\dfrac{-20}{-20}}{\dfrac{113}{10}}}{\dfrac{111}{4}}}}{\dfrac{-\dfrac{83}{3}}{-\dfrac{20}{11}}}}{16}-\left(-10\right)\times\left(-\dfrac{349}{3}\right)\times\dfrac{149}{8}-\dfrac{351}{4}-\dfrac{344}{15}-\dfrac{344}{15}\right)}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{28}{15}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{-17}{-\dfrac{20}{11}}}{\left(-\dfrac{349}{3}\right)\times\left(-20\right)\times\dfrac{113}{10}\times\left(-\dfrac{49}{19}\right)}}{\dfrac{344}{15}}}{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{349}{3}}{\dfrac{28}{15}}}{-\dfrac{49}{19}}}{-\dfrac{49}{19}}}{\dfrac{344}{15}}}}}{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{83}{3}}{\dfrac{113}{10}}}{-10}}{-\dfrac{173}{2}}}{\dfrac{309}{11}}\times\left(\dfrac{149}{8}-20+16+\dfrac{111}{4}-\dfrac{123}{14}\right)\times\dfrac{344}{15}\times\dfrac{309}{11}\times\dfrac{11}{2}\times0}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{28}{15}}{0}}{1-7}}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{344}{15}+\dfrac{4}{95779}+\dfrac{20}{49}-\dfrac{409}{12}}{-10}}{-\dfrac{173}{2}}}{\dfrac{149}{8}\times\dfrac{351}{4}\times\dfrac{71}{2}\times\dfrac{\dfrac{-\dfrac{42}{1411}}{-20}}{\dfrac{351}{4}}}-\left(\dfrac{\dfrac{\dfrac{\dfrac{1}{-20}}{\dfrac{\dfrac{\dfrac{-20}{-20}}{\dfrac{113}{10}}}{\dfrac{111}{4}}}}{\dfrac{-\dfrac{83}{3}}{-\dfrac{20}{11}}}}{16}-\left(-10\right)\times\left(-\dfrac{349}{3}\right)\times\dfrac{149}{8}-\dfrac{351}{4}-\dfrac{344}{15}-\dfrac{344}{15}\right)}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{28}{15}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{-17}{-\dfrac{20}{11}}}{\left(-\dfrac{349}{3}\right)\times\left(-20\right)\times\dfrac{113}{10}\times\left(-\dfrac{49}{19}\right)}}{\dfr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dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{28}{15}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{-17}{-\dfrac{20}{11}}}{-\dfrac{3864826}{57}}}{\dfrac{344}{15}}}{-\dfrac{9449175}{23126432}}}}{\dfrac{\dfrac{\dfrac{83}{339}}{-\dfrac{173}{2}}}{\dfrac{309}{11}}\times\left(\dfrac{149}{8}-20+16+\dfrac{111}{4}-\dfrac{123}{14}\right)\times\dfrac{344}{15}\times\dfrac{309}{11}\times\dfrac{11}{2}\times0}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{28}{15}}{0}}{1-7}}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{344}{15}+\dfrac{4}{95779}+\dfrac{20}{49}-\dfrac{409}{12}}{-10}}{-\dfrac{173}{2}}}{\dfrac{149}{8}\times\dfrac{351}{4}\times\dfrac{71}{2}\times\dfrac{14}{825435}}-\left(\dfrac{\dfrac{\dfrac{-\dfrac{1}{20}}{\dfrac{40}{12543}}}{\dfrac{913}{60}}}{16}-\left(-10\right)\times\left(-\dfrac{52001}{24}\right)-\dfrac{351}{4}-\dfrac{344}{15}-\dfrac{344}{15}\right)}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{28}{15}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{-17}{-\dfrac{20}{11}}}{-\dfrac{3864826}{57}}}{\dfrac{344}{15}}}{-\dfrac{9449175}{23126432}}}}{\dfrac{-\dfrac{166}{58647}}{\dfrac{309}{11}}\times\left(\dfrac{149}{8}-20+16+\dfrac{111}{4}-\dfrac{123}{14}\right)\times\dfrac{344}{15}\times\dfrac{309}{11}\times\dfrac{11}{2}\times0}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{28}{15}}{0}}{1-7}}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{344}{15}+\dfrac{4}{95779}+\dfrac{20}{49}-\dfrac{409}{12}}{-10}}{-\dfrac{173}{2}}}{\dfrac{149}{8}\times\dfrac{351}{4}\times\dfrac{71}{2}\times\dfrac{14}{825435}}-\left(\dfrac{\dfrac{\dfrac{-\dfrac{1}{20}}{\dfrac{40}{12543}}}{\dfrac{913}{60}}}{16}-\left(-10\right)\times\left(-\dfrac{52001}{24}\right)-\dfrac{351}{4}-\dfrac{344}{15}-\dfrac{344}{15}\right)}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{28}{15}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{-17}{-\dfrac{20}{11}}}{-\dfrac{3864826}{57}}}{\dfrac{344}{15}}}{-\dfrac{9449175}{23126432}}}}{\left(-\dfrac{1826}{18121923}\right)\times\left(\dfrac{149}{8}-20+16+\dfrac{111}{4}-\dfrac{123}{14}\right)\times\dfrac{344}{15}\times\dfrac{309}{11}\times\dfrac{11}{2}\times0}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{28}{15}}{0}}{1-7}}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{344}{15}+\dfrac{4}{95779}+\dfrac{20}{49}-\dfrac{409}{12}}{-10}}{-\dfrac{173}{2}}}{\dfrac{149}{8}\times\dfrac{351}{4}\times\dfrac{71}{2}\times\dfrac{14}{825435}}-\left(\dfrac{\dfrac{\dfrac{-\dfrac{1}{20}}{\dfrac{40}{12543}}}{\dfrac{913}{60}}}{16}-\left(-10\right)\times\left(-\dfrac{52001}{24}\right)-\dfrac{351}{4}-\dfrac{344}{15}-\dfrac{344}{15}\right)}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{28}{15}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{-17}{-\dfrac{20}{11}}}{-\dfrac{3864826}{57}}}{\dfrac{344}{15}}}{-\dfrac{9449175}{23126432}}}}{\left(-\dfrac{1826}{18121923}\right)\times\left(-\dfrac{11}{8}+16+\dfrac{111}{4}-\dfrac{123}{14}\right)\times\dfrac{344}{15}\times\dfrac{309}{11}\times\dfrac{11}{2}\times0}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{28}{15}}{0}}{1-7}}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{344}{15}+\dfrac{4}{95779}+\dfrac{20}{49}-\dfrac{409}{12}}{-10}}{-\dfrac{173}{2}}}{\dfrac{149}{8}\times\dfrac{351}{4}\times\dfrac{71}{2}\times\dfrac{14}{825435}}-\left(\dfrac{\dfrac{\dfrac{-\dfrac{1}{20}}{\dfrac{40}{12543}}}{\dfrac{913}{60}}}{16}-\left(-10\right)\times\left(-\dfrac{52001}{24}\right)-\dfrac{351}{4}-\dfrac{344}{15}-\dfrac{344}{15}\right)}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{28}{15}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{-17}{-\dfrac{20}{11}}}{-\dfrac{3864826}{57}}}{\dfrac{344}{15}}}{-\dfrac{9449175}{23126432}}}}{\left(-\dfrac{1826}{18121923}\right)\times\left(\dfrac{117}{8}+\dfrac{111}{4}-\dfrac{123}{14}\right)\times\dfrac{344}{15}\times\dfrac{309}{11}\times\dfrac{11}{2}\times0}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{28}{15}}{0}}{1-7}}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{\dfrac{\dfrac{\dfrac{\dfrac{344}{15}+\dfrac{4}{95779}+\dfrac{20}{49}-\dfrac{409}{12}}{-10}}{-\dfrac{173}{2}}}{\dfrac{149}{8}\times\dfrac{351}{4}\times\dfrac{71}{2}\times\dfrac{14}{825435}}-\left(\dfrac{\dfrac{\dfrac{-\dfrac{1}{20}}{\dfrac{40}{12543}}}{\dfrac{913}{60}}}{16}-\left(-10\right)\times\left(-\dfrac{52001}{24}\right)-\dfrac{351}{4}-\dfrac{344}{15}-\dfrac{344}{15}\right)}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{2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6}}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{-\dfrac{4097252551515840}{324675036865254600}+\dfrac{137577124652400}{6310656000}}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{\dfrac{\dfrac{2}{71}}{\dfrac{3697569580320}{251253590463624000}}}{0}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{28}{15}}{0}}{-6}}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{-\dfrac{4097252551515840}{324675036865254600}+\dfrac{137577124652400}{6310656000}}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{\dfrac{\dfrac{502507180927248000}{262527440202720}}{0}}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{28}{15}}{0}}{-6}}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{-\dfrac{4097252551515840}{324675036865254600}+\dfrac{137577124652400}{6310656000}}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{0}}{\dfrac{71}{2}}}{\dfrac{\dfrac{\dfrac{28}{15}}{0}}{-6}}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{-\dfrac{4097252551515840}{324675036865254600}+\dfrac{137577124652400}{6310656000}}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{0}}{\dfrac{71}{2}}}{\dfrac{0}{-6}}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{-\dfrac{4097252551515840}{324675036865254600}+\dfrac{137577124652400}{6310656000}}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{0}}{\dfrac{71}{2}}}{0}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{\dfrac{4.4667832161982E+31}{2.0489124694439E+27}}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{28}{15}}{0}}{\dfrac{71}{2}}}{0}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{\dfrac{4.4667832161982E+31}{2.0489124694439E+27}}}{\dfrac{\dfrac{\dfrac{0}{\dfrac{71}{2}}}{0}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{\dfrac{4.4667832161982E+31}{2.0489124694439E+27}}}{\dfrac{\dfrac{0}{0}}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{\dfrac{4.4667832161982E+31}{2.0489124694439E+27}}}{\dfrac{0}{-\dfrac{83}{3}}}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{113}{10}}{\dfrac{11}{2}}}{\dfrac{4.4667832161982E+31}{2.0489124694439E+27}}}{0}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{\dfrac{113}{55}}{\dfrac{4.4667832161982E+31}{2.0489124694439E+27}}}{0}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&\dfrac{\dfrac{2.3152710904717E+29}{2.456730768909E+33}}{0}\times\left(8-10\right)\times\dfrac{351}{4}\\&=&0\times\left(8-10\right)\times\dfrac{351}{4}\\&=&0\times-2\times\dfrac{351}{4}\\&=&0\times\dfrac{351}{4}\\&=&0\\ \end{eqnarray*}