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 \[\dfrac{\dfrac{\dfrac{10}{7}}{\dfrac{133}{10}+\dfrac{103}{11}-\left(-\dfrac{57}{5}-\dfrac{\dfrac{\dfrac{68}{9}}{-2}}{\dfrac{65}{11}}\right)}}{\dfrac{65}{11}}-\dfrac{68}{9}\times\left(-\dfrac{57}{5}\right)\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{\dfrac{\dfrac{10}{7}}{\dfrac{133}{10}+\dfrac{103}{11}-\left(-\dfrac{57}{5}-\dfrac{\dfrac{\dfrac{68}{9}}{-2}}{\dfrac{65}{11}}\right)}}{\dfrac{65}{11}}-\dfrac{68}{9}\times\left(-\dfrac{57}{5}\right)=\dfrac{3890793224}{45167955}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{\dfrac{10}{7}}{\dfrac{133}{10}+\dfrac{103}{11}-\left(-\dfrac{57}{5}-\dfrac{-\dfrac{34}{9}}{\dfrac{65}{11}}\right)}}{\dfrac{65}{11}}-\dfrac{68}{9}\times\left(-\dfrac{57}{5}\right)\\&=&\dfrac{\dfrac{\dfrac{10}{7}}{\dfrac{133}{10}+\dfrac{103}{11}-\left(-\dfrac{57}{5}+\dfrac{374}{585}\right)}}{\dfrac{65}{11}}-\dfrac{68}{9}\times\left(-\dfrac{57}{5}\right)\\&=&\dfrac{\dfrac{\dfrac{10}{7}}{\dfrac{133}{10}+\dfrac{103}{11}+\dfrac{1259}{117}}}{\dfrac{65}{11}}-\dfrac{68}{9}\times\left(-\dfrac{57}{5}\right)\\&=&\dfrac{\dfrac{\dfrac{10}{7}}{\dfrac{2493}{110}+\dfrac{1259}{117}}}{\dfrac{65}{11}}-\dfrac{68}{9}\times\left(-\dfrac{57}{5}\right)\\&=&\dfrac{\dfrac{\dfrac{10}{7}}{\dfrac{430171}{12870}}}{\dfrac{65}{11}}-\dfrac{68}{9}\times\left(-\dfrac{57}{5}\right)\\&=&\dfrac{\dfrac{128700}{3011197}}{\dfrac{65}{11}}-\dfrac{68}{9}\times\left(-\dfrac{57}{5}\right)\\&=&\dfrac{21780}{3011197}-\dfrac{68}{9}\times\left(-\dfrac{57}{5}\right)\\&=&\dfrac{21780}{3011197}+\dfrac{1292}{15}\\&=&\dfrac{3890793224}{45167955}\\
\end{eqnarray*}