L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\dfrac{\dfrac{\dfrac{0}{-\dfrac{34}{7}-\dfrac{18}{11}-4+\dfrac{\dfrac{\dfrac{\dfrac{55}{2}}{9\times\left(-2\right)\times\dfrac{67}{5}\times0\times\left(-2+0\right)\times\left(-2\right)\times\left(9+2\right)}}{-2}}{-\dfrac{34}{7}-\dfrac{55}{2}+\dfrac{18}{11}-\dfrac{34}{7}}+\dfrac{67}{5}}}{-\dfrac{83}{8}}}{6}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{\dfrac{\dfrac{0}{-\dfrac{34}{7}-\dfrac{18}{11}-4+\dfrac{\dfrac{\dfrac{\dfrac{55}{2}}{9\times\left(-2\right)\times\dfrac{67}{5}\times0\times\left(-2+0\right)\times\left(-2\right)\times\left(9+2\right)}}{-2}}{-\dfrac{34}{7}-\dfrac{55}{2}+\dfrac{18}{11}-\dfrac{34}{7}}+\dfrac{67}{5}}}{-\dfrac{83}{8}}}{6}=0\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{\dfrac{0}{-\dfrac{34}{7}-\dfrac{18}{11}-4+\dfrac{\dfrac{\dfrac{\dfrac{55}{2}}{\left(-18\right)\times\dfrac{67}{5}\times0\times\left(-2+0\right)\times\left(-2\right)\times\left(9+2\right)}}{-2}}{-\dfrac{34}{7}-\dfrac{55}{2}+\dfrac{18}{11}-\dfrac{34}{7}}+\dfrac{67}{5}}}{-\dfrac{83}{8}}}{6}\\&=&\dfrac{\dfrac{\dfrac{0}{-\dfrac{34}{7}-\dfrac{18}{11}-4+\dfrac{\dfrac{\dfrac{\dfrac{55}{2}}{\left(-\dfrac{1206}{5}\right)\times0\times\left(-2+0\right)\times\left(-2\right)\times\left(9+2\right)}}{-2}}{-\dfrac{34}{7}-\dfrac{55}{2}+\dfrac{18}{11}-\dfrac{34}{7}}+\dfrac{67}{5}}}{-\dfrac{83}{8}}}{6}\\&=&\dfrac{\dfrac{\dfrac{0}{-\dfrac{34}{7}-\dfrac{18}{11}-4+\dfrac{\dfrac{\dfrac{\dfrac{55}{2}}{0\times\left(-2+0\right)\times\left(-2\right)\times\left(9+2\right)}}{-2}}{-\dfrac{34}{7}-\dfrac{55}{2}+\dfrac{18}{11}-\dfrac{34}{7}}+\dfrac{67}{5}}}{-\dfrac{83}{8}}}{6}\\&=&\dfrac{\dfrac{\dfrac{0}{-\dfrac{34}{7}-\dfrac{18}{11}-4+\dfrac{\dfrac{\dfrac{\dfrac{55}{2}}{0\times-2\times\left(-2\right)\times\left(9+2\right)}}{-2}}{-\dfrac{34}{7}-\dfrac{55}{2}+\dfrac{18}{11}-\dfrac{34}{7}}+\dfrac{67}{5}}}{-\dfrac{83}{8}}}{6}\\&=&\dfrac{\dfrac{\dfrac{0}{-\dfrac{34}{7}-\dfrac{18}{11}-4+\dfrac{\dfrac{\dfrac{\dfrac{55}{2}}{0\times-2\times\left(-2\right)\times11}}{-2}}{-\dfrac{34}{7}-\dfrac{55}{2}+\dfrac{18}{11}-\dfrac{34}{7}}+\dfrac{67}{5}}}{-\dfrac{83}{8}}}{6}\\&=&\dfrac{\dfrac{\dfrac{0}{-\dfrac{34}{7}-\dfrac{18}{11}-4+\dfrac{\dfrac{\dfrac{\dfrac{55}{2}}{0\times-2\times\left(-2\right)\times11}}{-2}}{-\dfrac{453}{14}+\dfrac{18}{11}-\dfrac{34}{7}}+\dfrac{67}{5}}}{-\dfrac{83}{8}}}{6}\\&=&\dfrac{\dfrac{\dfrac{0}{-\dfrac{34}{7}-\dfrac{18}{11}-4+\dfrac{\dfrac{\dfrac{\dfrac{55}{2}}{0\times-2\times\left(-2\right)\times11}}{-2}}{-\dfrac{4731}{154}-\dfrac{34}{7}}+\dfrac{67}{5}}}{-\dfrac{83}{8}}}{6}\\&=&\dfrac{\dfrac{\dfrac{0}{-\dfrac{34}{7}-\dfrac{18}{11}-4+\dfrac{\dfrac{\dfrac{\dfrac{55}{2}}{0\times\left(-2\right)\times11}}{-2}}{-\dfrac{4731}{154}-\dfrac{34}{7}}+\dfrac{67}{5}}}{-\dfrac{83}{8}}}{6}\\&=&\dfrac{\dfrac{\dfrac{0}{-\dfrac{34}{7}-\dfrac{18}{11}-4+\dfrac{\dfrac{\dfrac{\dfrac{55}{2}}{0\times11}}{-2}}{-\dfrac{4731}{154}-\dfrac{34}{7}}+\dfrac{67}{5}}}{-\dfrac{83}{8}}}{6}\\&=&\dfrac{\dfrac{\dfrac{0}{-\dfrac{34}{7}-\dfrac{18}{11}-4+\dfrac{\dfrac{\dfrac{\dfrac{55}{2}}{0}}{-2}}{-\dfrac{4731}{154}-\dfrac{34}{7}}+\dfrac{67}{5}}}{-\dfrac{83}{8}}}{6}\\&=&\dfrac{\dfrac{\dfrac{0}{-\dfrac{34}{7}-\dfrac{18}{11}-4+\dfrac{\dfrac{\dfrac{\dfrac{55}{2}}{0}}{-2}}{-\dfrac{5479}{154}}+\dfrac{67}{5}}}{-\dfrac{83}{8}}}{6}\\&=&\dfrac{\dfrac{\dfrac{0}{-\dfrac{34}{7}-\dfrac{62}{11}+\dfrac{\dfrac{\dfrac{\dfrac{55}{2}}{0}}{-2}}{-\dfrac{5479}{154}}+\dfrac{67}{5}}}{-\dfrac{83}{8}}}{6}\\&=&\dfrac{\dfrac{\dfrac{0}{-\dfrac{34}{7}-\dfrac{62}{11}+\dfrac{\dfrac{0}{-2}}{-\dfrac{5479}{154}}+\dfrac{67}{5}}}{-\dfrac{83}{8}}}{6}\\&=&\dfrac{\dfrac{\dfrac{0}{-\dfrac{34}{7}-\dfrac{62}{11}+\dfrac{0}{-\dfrac{5479}{154}}+\dfrac{67}{5}}}{-\dfrac{83}{8}}}{6}\\&=&\dfrac{\dfrac{\dfrac{0}{-\dfrac{34}{7}-\dfrac{62}{11}+0+\dfrac{67}{5}}}{-\dfrac{83}{8}}}{6}\\&=&\dfrac{\dfrac{\dfrac{0}{-\dfrac{808}{77}+0+\dfrac{67}{5}}}{-\dfrac{83}{8}}}{6}\\&=&\dfrac{\dfrac{\dfrac{0}{-\dfrac{808}{77}+\dfrac{67}{5}}}{-\dfrac{83}{8}}}{6}\\&=&\dfrac{\dfrac{\dfrac{0}{\dfrac{1119}{385}}}{-\dfrac{83}{8}}}{6}\\&=&\dfrac{\dfrac{0}{-\dfrac{83}{8}}}{6}\\&=&\dfrac{0}{6}\\&=&0\\
\end{eqnarray*}