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 \[\dfrac{\dfrac{\dfrac{-\dfrac{113}{4}}{-13}}{15\times\dfrac{-8}{\dfrac{263}{15}}}}{\dfrac{\dfrac{\dfrac{-13}{\dfrac{341}{18}}}{-12+\dfrac{113}{4}+4-\dfrac{113}{4}+\dfrac{69}{8}}}{15}}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{\dfrac{\dfrac{-\dfrac{113}{4}}{-13}}{15\times\dfrac{-8}{\dfrac{263}{15}}}}{\dfrac{\dfrac{\dfrac{-13}{\dfrac{341}{18}}}{-12+\dfrac{113}{4}+4-\dfrac{113}{4}+\dfrac{69}{8}}}{15}}=\dfrac{10134179}{2336256}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{\dfrac{-\dfrac{113}{4}}{-13}}{15\times\dfrac{-8}{\dfrac{263}{15}}}}{\dfrac{\dfrac{\dfrac{-13}{\dfrac{341}{18}}}{\dfrac{65}{4}+4-\dfrac{113}{4}+\dfrac{69}{8}}}{15}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{113}{4}}{-13}}{15\times\dfrac{-8}{\dfrac{263}{15}}}}{\dfrac{\dfrac{\dfrac{-13}{\dfrac{341}{18}}}{\dfrac{81}{4}-\dfrac{113}{4}+\dfrac{69}{8}}}{15}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{113}{4}}{-13}}{15\times\dfrac{-8}{\dfrac{263}{15}}}}{\dfrac{\dfrac{\dfrac{-13}{\dfrac{341}{18}}}{-8+\dfrac{69}{8}}}{15}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{113}{4}}{-13}}{15\times\left(-\dfrac{120}{263}\right)}}{\dfrac{\dfrac{\dfrac{-13}{\dfrac{341}{18}}}{-8+\dfrac{69}{8}}}{15}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{113}{4}}{-13}}{15\times\left(-\dfrac{120}{263}\right)}}{\dfrac{\dfrac{-\dfrac{234}{341}}{-8+\dfrac{69}{8}}}{15}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{113}{4}}{-13}}{15\times\left(-\dfrac{120}{263}\right)}}{\dfrac{\dfrac{-\dfrac{234}{341}}{\dfrac{5}{8}}}{15}}\\&=&\dfrac{\dfrac{\dfrac{113}{52}}{15\times\left(-\dfrac{120}{263}\right)}}{\dfrac{\dfrac{-\dfrac{234}{341}}{\dfrac{5}{8}}}{15}}\\&=&\dfrac{\dfrac{\dfrac{113}{52}}{-\dfrac{1800}{263}}}{\dfrac{\dfrac{-\dfrac{234}{341}}{\dfrac{5}{8}}}{15}}\\&=&\dfrac{\dfrac{\dfrac{113}{52}}{-\dfrac{1800}{263}}}{\dfrac{-\dfrac{1872}{1705}}{15}}\\&=&\dfrac{\dfrac{\dfrac{113}{52}}{-\dfrac{1800}{263}}}{-\dfrac{624}{8525}}\\&=&\dfrac{-\dfrac{29719}{93600}}{-\dfrac{624}{8525}}\\&=&\dfrac{10134179}{2336256}\\
\end{eqnarray*}