L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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Exercice
Calculer \[\left(-8\right)\times\left(-11-\dfrac{\dfrac{\dfrac{-10}{-10}}{\dfrac{16}{5}\times\left(-2\right)}}{\dfrac{14}{5}}-\dfrac{86}{11}\right)\times\left(-11\right)\times\dfrac{52}{11}\times\dfrac{52}{11}\times\left(\dfrac{86}{11}+\dfrac{11}{2}+\dfrac{9}{10}-\dfrac{14}{5}+11+\dfrac{43}{12}-10-\dfrac{43}{12}-\dfrac{11}{2}\right)\times\dfrac{86}{11}\]
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Exercice
On a \( X=\left(-8\right)\times\left(-11-\dfrac{\dfrac{\dfrac{-10}{-10}}{\dfrac{16}{5}\times\left(-2\right)}}{\dfrac{14}{5}}-\dfrac{86}{11}\right)\times\left(-11\right)\times\dfrac{52}{11}\times\dfrac{52}{11}\times\left(\dfrac{86}{11}+\dfrac{11}{2}+\dfrac{9}{10}-\dfrac{14}{5}+11+\dfrac{43}{12}-10-\dfrac{43}{12}-\dfrac{11}{2}\right)\times\dfrac{86}{11}=-\dfrac{8181225923312}{4099480}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(-8\right)\times\left(-11-\dfrac{\dfrac{\dfrac{-10}{-10}}{-\dfrac{32}{5}}}{\dfrac{14}{5}}-\dfrac{86}{11}\right)\times\left(-11\right)\times\dfrac{52}{11}\times\dfrac{52}{11}\times\left(\dfrac{86}{11}+\dfrac{11}{2}+\dfrac{9}{10}-\dfrac{14}{5}+11+\dfrac{43}{12}-10-\dfrac{43}{12}-\dfrac{11}{2}\right)\times\dfrac{86}{11}\\&=&\left(-8\right)\times\left(-11-\dfrac{\dfrac{\dfrac{-10}{-10}}{-\dfrac{32}{5}}}{\dfrac{14}{5}}-\dfrac{86}{11}\right)\times\left(-11\right)\times\dfrac{52}{11}\times\dfrac{52}{11}\times\left(\dfrac{86}{11}+\dfrac{11}{2}-\dfrac{19}{10}+11+\dfrac{43}{12}-10-\dfrac{43}{12}-\dfrac{11}{2}\right)\times\dfrac{86}{11}\\&=&\left(-8\right)\times\left(-11-\dfrac{\dfrac{\dfrac{-10}{-10}}{-\dfrac{32}{5}}}{\dfrac{14}{5}}-\dfrac{86}{11}\right)\times\left(-11\right)\times\dfrac{52}{11}\times\dfrac{52}{11}\times\left(\dfrac{86}{11}+\dfrac{11}{2}+\dfrac{91}{10}+\dfrac{43}{12}-10-\dfrac{43}{12}-\dfrac{11}{2}\right)\times\dfrac{86}{11}\\&=&\left(-8\right)\times\left(-11-\dfrac{\dfrac{\dfrac{-10}{-10}}{-\dfrac{32}{5}}}{\dfrac{14}{5}}-\dfrac{86}{11}\right)\times\left(-11\right)\times\dfrac{52}{11}\times\dfrac{52}{11}\times\left(\dfrac{86}{11}+\dfrac{11}{2}+\dfrac{91}{10}-\dfrac{77}{12}-\dfrac{43}{12}-\dfrac{11}{2}\right)\times\dfrac{86}{11}\\&=&\left(-8\right)\times\left(-11-\dfrac{\dfrac{\dfrac{-10}{-10}}{-\dfrac{32}{5}}}{\dfrac{14}{5}}-\dfrac{86}{11}\right)\times\left(-11\right)\times\dfrac{52}{11}\times\dfrac{52}{11}\times\left(\dfrac{86}{11}+\dfrac{11}{2}+\dfrac{91}{10}-10-\dfrac{11}{2}\right)\times\dfrac{86}{11}\\&=&\left(-8\right)\times\left(-11-\dfrac{\dfrac{\dfrac{-10}{-10}}{-\dfrac{32}{5}}}{\dfrac{14}{5}}-\dfrac{86}{11}\right)\times\left(-11\right)\times\dfrac{52}{11}\times\dfrac{52}{11}\times\left(\dfrac{86}{11}+\dfrac{11}{2}+\dfrac{91}{10}-\dfrac{31}{2}\right)\times\dfrac{86}{11}\\&=&\left(-8\right)\times\left(-11-\dfrac{\dfrac{1}{-\dfrac{32}{5}}}{\dfrac{14}{5}}-\dfrac{86}{11}\right)\times\left(-11\right)\times\dfrac{52}{11}\times\dfrac{52}{11}\times\left(\dfrac{86}{11}+\dfrac{11}{2}+\dfrac{91}{10}-\dfrac{31}{2}\right)\times\dfrac{86}{11}\\&=&\left(-8\right)\times\left(-11-\dfrac{-\dfrac{5}{32}}{\dfrac{14}{5}}-\dfrac{86}{11}\right)\times\left(-11\right)\times\dfrac{52}{11}\times\dfrac{52}{11}\times\left(\dfrac{86}{11}+\dfrac{11}{2}+\dfrac{91}{10}-\dfrac{31}{2}\right)\times\dfrac{86}{11}\\&=&\left(-8\right)\times\left(-11-\dfrac{-\dfrac{5}{32}}{\dfrac{14}{5}}-\dfrac{86}{11}\right)\times\left(-11\right)\times\dfrac{52}{11}\times\dfrac{52}{11}\times\left(\dfrac{86}{11}+\dfrac{11}{2}-\dfrac{32}{5}\right)\times\dfrac{86}{11}\\&=&\left(-8\right)\times\left(-11+\dfrac{25}{448}-\dfrac{86}{11}\right)\times\left(-11\right)\times\dfrac{52}{11}\times\dfrac{52}{11}\times\left(\dfrac{86}{11}+\dfrac{11}{2}-\dfrac{32}{5}\right)\times\dfrac{86}{11}\\&=&\left(-8\right)\times\left(-11+\dfrac{25}{448}-\dfrac{86}{11}\right)\times\left(-11\right)\times\dfrac{52}{11}\times\dfrac{52}{11}\times\left(\dfrac{293}{22}-\dfrac{32}{5}\right)\times\dfrac{86}{11}\\&=&\left(-8\right)\times\left(-11+\dfrac{25}{448}-\dfrac{86}{11}\right)\times\left(-11\right)\times\dfrac{52}{11}\times\dfrac{52}{11}\times\dfrac{761}{110}\times\dfrac{86}{11}\\&=&\left(-8\right)\times\left(-\dfrac{4903}{448}-\dfrac{86}{11}\right)\times\left(-11\right)\times\dfrac{52}{11}\times\dfrac{52}{11}\times\dfrac{761}{110}\times\dfrac{86}{11}\\&=&\left(-8\right)\times-\dfrac{92461}{4928}\times\left(-11\right)\times\dfrac{52}{11}\times\dfrac{52}{11}\times\dfrac{761}{110}\times\dfrac{86}{11}\\&=&\left(-8\right)\times-\dfrac{92461}{4928}\times\left(-11\right)\times\dfrac{2704}{121}\times\dfrac{761}{110}\times\dfrac{86}{11}\\&=&\left(-8\right)\times-\dfrac{92461}{4928}\times\left(-11\right)\times\dfrac{1028872}{6655}\times\dfrac{86}{11}\\&=&\left(-8\right)\times-\dfrac{92461}{4928}\times\left(-11\right)\times\dfrac{88482992}{73205}\\&=&\dfrac{92461}{616}\times\left(-11\right)\times\dfrac{88482992}{73205}\\&=&\left(-\dfrac{92461}{56}\right)\times\dfrac{88482992}{73205}\\&=&-\dfrac{8181225923312}{4099480}\\
\end{eqnarray*}