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 \[\dfrac{\left(-5\right)\times\left(-\dfrac{95}{3}\right)\times\dfrac{97}{6}\times\left(-5\right)\times\dfrac{97}{6}}{\dfrac{\dfrac{-\dfrac{5}{6}}{-\dfrac{89}{3}}}{-2+\dfrac{5}{6}}}-\dfrac{27}{11}+\dfrac{34}{5}+12\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{\left(-5\right)\times\left(-\dfrac{95}{3}\right)\times\dfrac{97}{6}\times\left(-5\right)\times\dfrac{97}{6}}{\dfrac{\dfrac{-\dfrac{5}{6}}{-\dfrac{89}{3}}}{-2+\dfrac{5}{6}}}-\dfrac{27}{11}+\dfrac{34}{5}+12=\dfrac{765699995755}{89100}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{475}{3}\times\dfrac{97}{6}\times\left(-5\right)\times\dfrac{97}{6}}{\dfrac{\dfrac{-\dfrac{5}{6}}{-\dfrac{89}{3}}}{-2+\dfrac{5}{6}}}-\dfrac{27}{11}+\dfrac{34}{5}+12\\&=&\dfrac{\dfrac{46075}{18}\times\left(-5\right)\times\dfrac{97}{6}}{\dfrac{\dfrac{-\dfrac{5}{6}}{-\dfrac{89}{3}}}{-2+\dfrac{5}{6}}}-\dfrac{27}{11}+\dfrac{34}{5}+12\\&=&\dfrac{\dfrac{46075}{18}\times\left(-5\right)\times\dfrac{97}{6}}{\dfrac{\dfrac{5}{178}}{-2+\dfrac{5}{6}}}-\dfrac{27}{11}+\dfrac{34}{5}+12\\&=&\dfrac{\dfrac{46075}{18}\times\left(-5\right)\times\dfrac{97}{6}}{\dfrac{\dfrac{5}{178}}{-\dfrac{7}{6}}}-\dfrac{27}{11}+\dfrac{34}{5}+12\\&=&\dfrac{\left(-\dfrac{230375}{18}\right)\times\dfrac{97}{6}}{\dfrac{\dfrac{5}{178}}{-\dfrac{7}{6}}}-\dfrac{27}{11}+\dfrac{34}{5}+12\\&=&\dfrac{-\dfrac{22346375}{108}}{\dfrac{\dfrac{5}{178}}{-\dfrac{7}{6}}}-\dfrac{27}{11}+\dfrac{34}{5}+12\\&=&\dfrac{-\dfrac{22346375}{108}}{-\dfrac{15}{623}}-\dfrac{27}{11}+\dfrac{34}{5}+12\\&=&\dfrac{13921791625}{1620}-\dfrac{27}{11}+\dfrac{34}{5}+12\\&=&\dfrac{153139664135}{17820}+\dfrac{34}{5}+12\\&=&\dfrac{765698926555}{89100}+12\\&=&\dfrac{765699995755}{89100}\\
\end{eqnarray*}