L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\dfrac{\dfrac{\dfrac{11}{4}}{\dfrac{1}{5}\times\left(-\dfrac{129}{11}\right)}}{\left(-6-\dfrac{\dfrac{1}{5}}{-6}+\dfrac{129}{11}\right)+\dfrac{104}{3}-\left(-7-\dfrac{104}{3}\right)}\times\dfrac{\dfrac{11}{4}}{7}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{\dfrac{\dfrac{11}{4}}{\dfrac{1}{5}\times\left(-\dfrac{129}{11}\right)}}{\left(-6-\dfrac{\dfrac{1}{5}}{-6}+\dfrac{129}{11}\right)+\dfrac{104}{3}-\left(-7-\dfrac{104}{3}\right)}\times\dfrac{\dfrac{11}{4}}{7}=-\dfrac{366025}{65235128}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{\dfrac{11}{4}}{\dfrac{1}{5}\times\left(-\dfrac{129}{11}\right)}}{\left(-6+\dfrac{1}{30}+\dfrac{129}{11}\right)+\dfrac{104}{3}-\left(-7-\dfrac{104}{3}\right)}\times\dfrac{\dfrac{11}{4}}{7}\\&=&\dfrac{\dfrac{\dfrac{11}{4}}{\dfrac{1}{5}\times\left(-\dfrac{129}{11}\right)}}{\left(-\dfrac{179}{30}+\dfrac{129}{11}\right)+\dfrac{104}{3}-\left(-7-\dfrac{104}{3}\right)}\times\dfrac{\dfrac{11}{4}}{7}\\&=&\dfrac{\dfrac{\dfrac{11}{4}}{\dfrac{1}{5}\times\left(-\dfrac{129}{11}\right)}}{\dfrac{1901}{330}+\dfrac{104}{3}-\left(-7-\dfrac{104}{3}\right)}\times\dfrac{\dfrac{11}{4}}{7}\\&=&\dfrac{\dfrac{\dfrac{11}{4}}{\dfrac{1}{5}\times\left(-\dfrac{129}{11}\right)}}{\dfrac{1901}{330}+\dfrac{104}{3}+\dfrac{125}{3}}\times\dfrac{\dfrac{11}{4}}{7}\\&=&\dfrac{\dfrac{\dfrac{11}{4}}{-\dfrac{129}{55}}}{\dfrac{1901}{330}+\dfrac{104}{3}+\dfrac{125}{3}}\times\dfrac{\dfrac{11}{4}}{7}\\&=&\dfrac{\dfrac{\dfrac{11}{4}}{-\dfrac{129}{55}}}{\dfrac{4447}{110}+\dfrac{125}{3}}\times\dfrac{\dfrac{11}{4}}{7}\\&=&\dfrac{\dfrac{\dfrac{11}{4}}{-\dfrac{129}{55}}}{\dfrac{27091}{330}}\times\dfrac{\dfrac{11}{4}}{7}\\&=&\dfrac{-\dfrac{605}{516}}{\dfrac{27091}{330}}\times\dfrac{\dfrac{11}{4}}{7}\\&=&\left(-\dfrac{33275}{2329826}\right)\times\dfrac{\dfrac{11}{4}}{7}\\&=&\left(-\dfrac{33275}{2329826}\right)\times\dfrac{11}{28}\\&=&-\dfrac{366025}{65235128}\\
\end{eqnarray*}