L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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Exercice
Calculer \[\dfrac{\dfrac{\dfrac{-\dfrac{20}{3}-7-7}{-12}}{\dfrac{128}{11}\times\left(-\dfrac{20}{3}\right)\times\left(-\dfrac{13}{6}\right)}}{\left(-\dfrac{20}{3}\right)\times7\times\left(-\dfrac{55}{6}\right)}\times\left(-11\right)\times\left(-\dfrac{13}{6}\right)\times\left(-\dfrac{20}{3}\right)\times\left(-\dfrac{13}{6}\right)\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{\dfrac{\dfrac{-\dfrac{20}{3}-7-7}{-12}}{\dfrac{128}{11}\times\left(-\dfrac{20}{3}\right)\times\left(-\dfrac{13}{6}\right)}}{\left(-\dfrac{20}{3}\right)\times7\times\left(-\dfrac{55}{6}\right)}\times\left(-11\right)\times\left(-\dfrac{13}{6}\right)\times\left(-\dfrac{20}{3}\right)\times\left(-\dfrac{13}{6}\right)=\dfrac{4433}{537600}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{\dfrac{-\dfrac{41}{3}-7}{-12}}{\dfrac{128}{11}\times\left(-\dfrac{20}{3}\right)\times\left(-\dfrac{13}{6}\right)}}{\left(-\dfrac{20}{3}\right)\times7\times\left(-\dfrac{55}{6}\right)}\times\left(-11\right)\times\left(-\dfrac{13}{6}\right)\times\left(-\dfrac{20}{3}\right)\times\left(-\dfrac{13}{6}\right)\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{62}{3}}{-12}}{\dfrac{128}{11}\times\left(-\dfrac{20}{3}\right)\times\left(-\dfrac{13}{6}\right)}}{\left(-\dfrac{20}{3}\right)\times7\times\left(-\dfrac{55}{6}\right)}\times\left(-11\right)\times\left(-\dfrac{13}{6}\right)\times\left(-\dfrac{20}{3}\right)\times\left(-\dfrac{13}{6}\right)\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{62}{3}}{-12}}{\left(-\dfrac{2560}{33}\right)\times\left(-\dfrac{13}{6}\right)}}{\left(-\dfrac{20}{3}\right)\times7\times\left(-\dfrac{55}{6}\right)}\times\left(-11\right)\times\left(-\dfrac{13}{6}\right)\times\left(-\dfrac{20}{3}\right)\times\left(-\dfrac{13}{6}\right)\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{62}{3}}{-12}}{\dfrac{16640}{99}}}{\left(-\dfrac{20}{3}\right)\times7\times\left(-\dfrac{55}{6}\right)}\times\left(-11\right)\times\left(-\dfrac{13}{6}\right)\times\left(-\dfrac{20}{3}\right)\times\left(-\dfrac{13}{6}\right)\\&=&\dfrac{\dfrac{\dfrac{31}{18}}{\dfrac{16640}{99}}}{\left(-\dfrac{20}{3}\right)\times7\times\left(-\dfrac{55}{6}\right)}\times\left(-11\right)\times\left(-\dfrac{13}{6}\right)\times\left(-\dfrac{20}{3}\right)\times\left(-\dfrac{13}{6}\right)\\&=&\dfrac{\dfrac{341}{33280}}{\left(-\dfrac{20}{3}\right)\times7\times\left(-\dfrac{55}{6}\right)}\times\left(-11\right)\times\left(-\dfrac{13}{6}\right)\times\left(-\dfrac{20}{3}\right)\times\left(-\dfrac{13}{6}\right)\\&=&\dfrac{\dfrac{341}{33280}}{\left(-\dfrac{140}{3}\right)\times\left(-\dfrac{55}{6}\right)}\times\left(-11\right)\times\left(-\dfrac{13}{6}\right)\times\left(-\dfrac{20}{3}\right)\times\left(-\dfrac{13}{6}\right)\\&=&\dfrac{\dfrac{341}{33280}}{\dfrac{3850}{9}}\times\left(-11\right)\times\left(-\dfrac{13}{6}\right)\times\left(-\dfrac{20}{3}\right)\times\left(-\dfrac{13}{6}\right)\\&=&\dfrac{279}{11648000}\times\left(-11\right)\times\left(-\dfrac{13}{6}\right)\times\left(-\dfrac{20}{3}\right)\times\left(-\dfrac{13}{6}\right)\\&=&\left(-\dfrac{3069}{11648000}\right)\times\left(-\dfrac{13}{6}\right)\times\left(-\dfrac{20}{3}\right)\times\left(-\dfrac{13}{6}\right)\\&=&\dfrac{1023}{1792000}\times\left(-\dfrac{20}{3}\right)\times\left(-\dfrac{13}{6}\right)\\&=&\left(-\dfrac{341}{89600}\right)\times\left(-\dfrac{13}{6}\right)\\&=&\dfrac{4433}{537600}\\
\end{eqnarray*}