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 \[\dfrac{\dfrac{\dfrac{-\dfrac{61}{5}}{\dfrac{37}{3}}}{\dfrac{\left(\left(-\dfrac{61}{5}\right)\times\dfrac{136}{9}-\dfrac{37}{3}\right)-\left(\dfrac{37}{3}-\dfrac{13}{2}+\dfrac{69}{5}+3\right)}{3}}}{\dfrac{39}{4}}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{\dfrac{\dfrac{-\dfrac{61}{5}}{\dfrac{37}{3}}}{\dfrac{\left(\left(-\dfrac{61}{5}\right)\times\dfrac{136}{9}-\dfrac{37}{3}\right)-\left(\dfrac{37}{3}-\dfrac{13}{2}+\dfrac{69}{5}+3\right)}{3}}}{\dfrac{39}{4}}=\dfrac{13176}{9494459}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{\dfrac{-\dfrac{61}{5}}{\dfrac{37}{3}}}{\dfrac{\left(-\dfrac{8296}{45}-\dfrac{37}{3}\right)-\left(\dfrac{37}{3}-\dfrac{13}{2}+\dfrac{69}{5}+3\right)}{3}}}{\dfrac{39}{4}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{61}{5}}{\dfrac{37}{3}}}{\dfrac{\left(-\dfrac{8296}{45}-\dfrac{37}{3}\right)-\left(\dfrac{35}{6}+\dfrac{69}{5}+3\right)}{3}}}{\dfrac{39}{4}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{61}{5}}{\dfrac{37}{3}}}{\dfrac{\left(-\dfrac{8296}{45}-\dfrac{37}{3}\right)-\left(\dfrac{589}{30}+3\right)}{3}}}{\dfrac{39}{4}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{61}{5}}{\dfrac{37}{3}}}{\dfrac{-\dfrac{8851}{45}-\left(\dfrac{589}{30}+3\right)}{3}}}{\dfrac{39}{4}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{61}{5}}{\dfrac{37}{3}}}{\dfrac{-\dfrac{8851}{45}-\dfrac{679}{30}}{3}}}{\dfrac{39}{4}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{61}{5}}{\dfrac{37}{3}}}{\dfrac{-\dfrac{19739}{90}}{3}}}{\dfrac{39}{4}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{61}{5}}{\dfrac{37}{3}}}{-\dfrac{19739}{270}}}{\dfrac{39}{4}}\\&=&\dfrac{\dfrac{-\dfrac{183}{185}}{-\dfrac{19739}{270}}}{\dfrac{39}{4}}\\&=&\dfrac{\dfrac{9882}{730343}}{\dfrac{39}{4}}\\&=&\dfrac{13176}{9494459}\\
\end{eqnarray*}