L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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Exercice
Calculer \[3-\left(-3+\dfrac{\dfrac{\dfrac{83}{10}}{\dfrac{\dfrac{\dfrac{3}{\dfrac{68}{5}}}{-8}}{11}}}{-2}-8+\dfrac{83}{10}-2-\dfrac{140}{11}+\dfrac{3}{7}+11\times\dfrac{85}{12}-\dfrac{51}{7}-\dfrac{140}{11}+\dfrac{\dfrac{3}{7}}{\left(-\dfrac{140}{11}\right)\times\left(-\dfrac{140}{11}+\dfrac{83}{10}\right)}\right)-\dfrac{85}{12}+\dfrac{51}{7}\]
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Exercice
On a \( X=3-\left(-3+\dfrac{\dfrac{\dfrac{83}{10}}{\dfrac{\dfrac{\dfrac{3}{\dfrac{68}{5}}}{-8}}{11}}}{-2}-8+\dfrac{83}{10}-2-\dfrac{140}{11}+\dfrac{3}{7}+11\times\dfrac{85}{12}-\dfrac{51}{7}-\dfrac{140}{11}+\dfrac{\dfrac{3}{7}}{\left(-\dfrac{140}{11}\right)\times\left(-\dfrac{140}{11}+\dfrac{83}{10}\right)}\right)-\dfrac{85}{12}+\dfrac{51}{7}=-\dfrac{52270268865472}{30869176800}\) . Voici le détail :
\begin{eqnarray*}
X &=&3-\left(-3+\dfrac{\dfrac{\dfrac{83}{10}}{\dfrac{\dfrac{\dfrac{15}{68}}{-8}}{11}}}{-2}-8+\dfrac{83}{10}-2-\dfrac{140}{11}+\dfrac{3}{7}+11\times\dfrac{85}{12}-\dfrac{51}{7}-\dfrac{140}{11}+\dfrac{\dfrac{3}{7}}{\left(-\dfrac{140}{11}\right)\times\left(-\dfrac{140}{11}+\dfrac{83}{10}\right)}\right)-\dfrac{85}{12}+\dfrac{51}{7}\\&=&3-\left(-3+\dfrac{\dfrac{\dfrac{83}{10}}{\dfrac{-\dfrac{15}{544}}{11}}}{-2}-8+\dfrac{83}{10}-2-\dfrac{140}{11}+\dfrac{3}{7}+11\times\dfrac{85}{12}-\dfrac{51}{7}-\dfrac{140}{11}+\dfrac{\dfrac{3}{7}}{\left(-\dfrac{140}{11}\right)\times\left(-\dfrac{140}{11}+\dfrac{83}{10}\right)}\right)-\dfrac{85}{12}+\dfrac{51}{7}\\&=&3-\left(-3+\dfrac{\dfrac{\dfrac{83}{10}}{-\dfrac{15}{5984}}}{-2}-8+\dfrac{83}{10}-2-\dfrac{140}{11}+\dfrac{3}{7}+11\times\dfrac{85}{12}-\dfrac{51}{7}-\dfrac{140}{11}+\dfrac{\dfrac{3}{7}}{\left(-\dfrac{140}{11}\right)\times\left(-\dfrac{140}{11}+\dfrac{83}{10}\right)}\right)-\dfrac{85}{12}+\dfrac{51}{7}\\&=&3-\left(-3+\dfrac{\dfrac{\dfrac{83}{10}}{-\dfrac{15}{5984}}}{-2}-8+\dfrac{83}{10}-\dfrac{162}{11}+\dfrac{3}{7}+11\times\dfrac{85}{12}-\dfrac{51}{7}-\dfrac{140}{11}+\dfrac{\dfrac{3}{7}}{\left(-\dfrac{140}{11}\right)\times\left(-\dfrac{140}{11}+\dfrac{83}{10}\right)}\right)-\dfrac{85}{12}+\dfrac{51}{7}\\&=&3-\left(-3+\dfrac{\dfrac{\dfrac{83}{10}}{-\dfrac{15}{5984}}}{-2}-8+\dfrac{83}{10}-\dfrac{1101}{77}+11\times\dfrac{85}{12}-\dfrac{51}{7}-\dfrac{140}{11}+\dfrac{\dfrac{3}{7}}{\left(-\dfrac{140}{11}\right)\times\left(-\dfrac{140}{11}+\dfrac{83}{10}\right)}\right)-\dfrac{85}{12}+\dfrac{51}{7}\\&=&3-\left(-3+\dfrac{\dfrac{\dfrac{83}{10}}{-\dfrac{15}{5984}}}{-2}-8+\dfrac{83}{10}-\dfrac{1101}{77}+\dfrac{935}{12}-\dfrac{51}{7}-\dfrac{140}{11}+\dfrac{\dfrac{3}{7}}{\left(-\dfrac{140}{11}\right)\times\left(-\dfrac{140}{11}+\dfrac{83}{10}\right)}\right)-\dfrac{85}{12}+\dfrac{51}{7}\\&=&3-\left(-3+\dfrac{\dfrac{\dfrac{83}{10}}{-\dfrac{15}{5984}}}{-2}-8+\dfrac{83}{10}-\dfrac{1101}{77}+\dfrac{935}{12}-\dfrac{51}{7}-\dfrac{140}{11}+\dfrac{\dfrac{3}{7}}{\left(-\dfrac{140}{11}\right)\times-\dfrac{487}{110}}\right)-\dfrac{85}{12}+\dfrac{51}{7}\\&=&3-\left(-3+\dfrac{-\dfrac{248336}{75}}{-2}-8+\dfrac{83}{10}-\dfrac{1101}{77}+\dfrac{935}{12}-\dfrac{51}{7}-\dfrac{140}{11}+\dfrac{\dfrac{3}{7}}{\left(-\dfrac{140}{11}\right)\times-\dfrac{487}{110}}\right)-\dfrac{85}{12}+\dfrac{51}{7}\\&=&3-\left(-3+\dfrac{124168}{75}-8+\dfrac{83}{10}-\dfrac{1101}{77}+\dfrac{935}{12}-\dfrac{51}{7}-\dfrac{140}{11}+\dfrac{\dfrac{3}{7}}{\left(-\dfrac{140}{11}\right)\times-\dfrac{487}{110}}\right)-\dfrac{85}{12}+\dfrac{51}{7}\\&=&3-\left(-3+\dfrac{124168}{75}-8-\dfrac{4619}{770}+\dfrac{935}{12}-\dfrac{51}{7}-\dfrac{140}{11}+\dfrac{\dfrac{3}{7}}{\left(-\dfrac{140}{11}\right)\times-\dfrac{487}{110}}\right)-\dfrac{85}{12}+\dfrac{51}{7}\\&=&3-\left(-3+\dfrac{124168}{75}-8+\dfrac{332261}{4620}-\dfrac{51}{7}-\dfrac{140}{11}+\dfrac{\dfrac{3}{7}}{\left(-\dfrac{140}{11}\right)\times-\dfrac{487}{110}}\right)-\dfrac{85}{12}+\dfrac{51}{7}\\&=&3-\left(-3+\dfrac{124168}{75}-8+\dfrac{332261}{4620}-\dfrac{51}{7}-\dfrac{140}{11}+\dfrac{\dfrac{3}{7}}{\dfrac{6818}{121}}\right)-\dfrac{85}{12}+\dfrac{51}{7}\\&=&3-\left(-3+\dfrac{123568}{75}+\dfrac{332261}{4620}-\dfrac{51}{7}-\dfrac{140}{11}+\dfrac{\dfrac{3}{7}}{\dfrac{6818}{121}}\right)-\dfrac{85}{12}+\dfrac{51}{7}\\&=&3-\left(-3+\dfrac{13240083}{7700}-\dfrac{51}{7}-\dfrac{140}{11}+\dfrac{\dfrac{3}{7}}{\dfrac{6818}{121}}\right)-\dfrac{85}{12}+\dfrac{51}{7}\\&=&3-\left(-3+\dfrac{13183983}{7700}-\dfrac{140}{11}+\dfrac{\dfrac{3}{7}}{\dfrac{6818}{121}}\right)-\dfrac{85}{12}+\dfrac{51}{7}\\&=&3-\left(-3+\dfrac{13183983}{7700}-\dfrac{140}{11}+\dfrac{363}{47726}\right)-\dfrac{85}{12}+\dfrac{51}{7}\\&=&3-\left(\dfrac{13160883}{7700}-\dfrac{140}{11}+\dfrac{363}{47726}\right)-\dfrac{85}{12}+\dfrac{51}{7}\\&=&3-\left(\dfrac{13062883}{7700}+\dfrac{363}{47726}\right)-\dfrac{85}{12}+\dfrac{51}{7}\\&=&3-\dfrac{623441949158}{367490200}-\dfrac{85}{12}+\dfrac{51}{7}\\&=&-\dfrac{622339478558}{367490200}-\dfrac{85}{12}+\dfrac{51}{7}\\&=&-\dfrac{7499310409696}{4409882400}+\dfrac{51}{7}\\&=&-\dfrac{52270268865472}{30869176800}\\
\end{eqnarray*}