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 \[\dfrac{\dfrac{\dfrac{\dfrac{73}{12}}{\dfrac{-10}{1\times1\times\dfrac{11}{3}}-12+\dfrac{73}{12}-\dfrac{78}{7}+\dfrac{142}{5}\times1\times1}}{3}}{-\dfrac{78}{7}}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{\dfrac{\dfrac{\dfrac{73}{12}}{\dfrac{-10}{1\times1\times\dfrac{11}{3}}-12+\dfrac{73}{12}-\dfrac{78}{7}+\dfrac{142}{5}\times1\times1}}{3}}{-\dfrac{78}{7}}=-\dfrac{196735}{9311562}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{\dfrac{\dfrac{73}{12}}{\dfrac{-10}{1\times\dfrac{11}{3}}-12+\dfrac{73}{12}-\dfrac{78}{7}+\dfrac{142}{5}\times1\times1}}{3}}{-\dfrac{78}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{73}{12}}{\dfrac{-10}{\dfrac{11}{3}}-12+\dfrac{73}{12}-\dfrac{78}{7}+\dfrac{142}{5}\times1\times1}}{3}}{-\dfrac{78}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{73}{12}}{\dfrac{-10}{\dfrac{11}{3}}-12+\dfrac{73}{12}-\dfrac{78}{7}+\dfrac{142}{5}\times1}}{3}}{-\dfrac{78}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{73}{12}}{-\dfrac{30}{11}-12+\dfrac{73}{12}-\dfrac{78}{7}+\dfrac{142}{5}\times1}}{3}}{-\dfrac{78}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{73}{12}}{-\dfrac{30}{11}-\dfrac{71}{12}-\dfrac{78}{7}+\dfrac{142}{5}\times1}}{3}}{-\dfrac{78}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{73}{12}}{-\dfrac{30}{11}-\dfrac{1433}{84}+\dfrac{142}{5}\times1}}{3}}{-\dfrac{78}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{73}{12}}{-\dfrac{30}{11}-\dfrac{1433}{84}+\dfrac{142}{5}}}{3}}{-\dfrac{78}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{73}{12}}{-\dfrac{18283}{924}+\dfrac{142}{5}}}{3}}{-\dfrac{78}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{73}{12}}{\dfrac{39793}{4620}}}{3}}{-\dfrac{78}{7}}\\&=&\dfrac{\dfrac{\dfrac{28105}{39793}}{3}}{-\dfrac{78}{7}}\\&=&\dfrac{\dfrac{28105}{119379}}{-\dfrac{78}{7}}\\&=&-\dfrac{196735}{9311562}\\
\end{eqnarray*}