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.
Calculer \[\dfrac{\dfrac{\dfrac{\dfrac{23}{4}-\dfrac{113}{5}}{\dfrac{308}{19}}}{\left(\left(\dfrac{\dfrac{131}{2}}{\dfrac{23}{19}}+\dfrac{241}{17}\right)-\left(-\dfrac{157}{13}\right)\times7\right)\times\dfrac{7}{12}}}{-\dfrac{29}{19}}\]
Cliquer ici pour afficher la solution
On a \( X=\dfrac{\dfrac{\dfrac{\dfrac{23}{4}-\dfrac{113}{5}}{\dfrac{308}{19}}}{\left(\left(\dfrac{\dfrac{131}{2}}{\dfrac{23}{19}}+\dfrac{241}{17}\right)-\left(-\dfrac{157}{13}\right)\times7\right)\times\dfrac{7}{12}}}{-\dfrac{29}{19}}=\dfrac{14841180744}{1942751980400}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{\dfrac{\dfrac{23}{4}-\dfrac{113}{5}}{\dfrac{308}{19}}}{\left(\left(\dfrac{2489}{46}+\dfrac{241}{17}\right)-\left(-\dfrac{157}{13}\right)\times7\right)\times\dfrac{7}{12}}}{-\dfrac{29}{19}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{23}{4}-\dfrac{113}{5}}{\dfrac{308}{19}}}{\left(\dfrac{53399}{782}-\left(-\dfrac{157}{13}\right)\times7\right)\times\dfrac{7}{12}}}{-\dfrac{29}{19}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{23}{4}-\dfrac{113}{5}}{\dfrac{308}{19}}}{\left(\dfrac{53399}{782}+\dfrac{1099}{13}\right)\times\dfrac{7}{12}}}{-\dfrac{29}{19}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{337}{20}}{\dfrac{308}{19}}}{\left(\dfrac{53399}{782}+\dfrac{1099}{13}\right)\times\dfrac{7}{12}}}{-\dfrac{29}{19}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{337}{20}}{\dfrac{308}{19}}}{\dfrac{1553605}{10166}\times\dfrac{7}{12}}}{-\dfrac{29}{19}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{337}{20}}{\dfrac{308}{19}}}{\dfrac{1553605}{10166}\times\dfrac{7}{12}}}{-\dfrac{29}{19}}\\&=&\dfrac{\dfrac{-\dfrac{6403}{6160}}{\dfrac{1553605}{10166}\times\dfrac{7}{12}}}{-\dfrac{29}{19}}\\&=&\dfrac{\dfrac{-\dfrac{6403}{6160}}{\dfrac{10875235}{121992}}}{-\dfrac{29}{19}}\\&=&\dfrac{-\dfrac{781114776}{66991447600}}{-\dfrac{29}{19}}\\&=&\dfrac{14841180744}{1942751980400}\\
\end{eqnarray*}