L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\left(-7\right)\times\dfrac{\dfrac{4}{\dfrac{\dfrac{-10}{\dfrac{39}{4}\times\dfrac{111}{11}}}{12}}}{\dfrac{39}{2}-\dfrac{\dfrac{111}{11}}{\dfrac{39}{4}-\dfrac{39}{11}}-\dfrac{\dfrac{\left(-2\right)\times8}{\dfrac{93}{4}}}{\dfrac{39}{4}}}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\left(-7\right)\times\dfrac{\dfrac{4}{\dfrac{\dfrac{-10}{\dfrac{39}{4}\times\dfrac{111}{11}}}{12}}}{\dfrac{39}{2}-\dfrac{\dfrac{111}{11}}{\dfrac{39}{4}-\dfrac{39}{11}}-\dfrac{\dfrac{\left(-2\right)\times8}{\dfrac{93}{4}}}{\dfrac{39}{4}}}=\dfrac{9232354404}{50114405}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(-7\right)\times\dfrac{\dfrac{4}{\dfrac{\dfrac{-10}{\dfrac{39}{4}\times\dfrac{111}{11}}}{12}}}{\dfrac{39}{2}-\dfrac{\dfrac{111}{11}}{\dfrac{273}{44}}-\dfrac{\dfrac{\left(-2\right)\times8}{\dfrac{93}{4}}}{\dfrac{39}{4}}}\\&=&\left(-7\right)\times\dfrac{\dfrac{4}{\dfrac{\dfrac{-10}{\dfrac{39}{4}\times\dfrac{111}{11}}}{12}}}{\dfrac{39}{2}-\dfrac{\dfrac{111}{11}}{\dfrac{273}{44}}-\dfrac{\dfrac{-16}{\dfrac{93}{4}}}{\dfrac{39}{4}}}\\&=&\left(-7\right)\times\dfrac{\dfrac{4}{\dfrac{\dfrac{-10}{\dfrac{4329}{44}}}{12}}}{\dfrac{39}{2}-\dfrac{\dfrac{111}{11}}{\dfrac{273}{44}}-\dfrac{\dfrac{-16}{\dfrac{93}{4}}}{\dfrac{39}{4}}}\\&=&\left(-7\right)\times\dfrac{\dfrac{4}{\dfrac{\dfrac{-10}{\dfrac{4329}{44}}}{12}}}{\dfrac{39}{2}-\dfrac{148}{91}-\dfrac{\dfrac{-16}{\dfrac{93}{4}}}{\dfrac{39}{4}}}\\&=&\left(-7\right)\times\dfrac{\dfrac{4}{\dfrac{\dfrac{-10}{\dfrac{4329}{44}}}{12}}}{\dfrac{39}{2}-\dfrac{148}{91}-\dfrac{-\dfrac{64}{93}}{\dfrac{39}{4}}}\\&=&\left(-7\right)\times\dfrac{\dfrac{4}{\dfrac{\dfrac{-10}{\dfrac{4329}{44}}}{12}}}{\dfrac{39}{2}-\dfrac{148}{91}+\dfrac{256}{3627}}\\&=&\left(-7\right)\times\dfrac{\dfrac{4}{\dfrac{-\dfrac{440}{4329}}{12}}}{\dfrac{39}{2}-\dfrac{148}{91}+\dfrac{256}{3627}}\\&=&\left(-7\right)\times\dfrac{\dfrac{4}{-\dfrac{110}{12987}}}{\dfrac{39}{2}-\dfrac{148}{91}+\dfrac{256}{3627}}\\&=&\left(-7\right)\times\dfrac{\dfrac{4}{-\dfrac{110}{12987}}}{\dfrac{3253}{182}+\dfrac{256}{3627}}\\&=&\left(-7\right)\times\dfrac{\dfrac{4}{-\dfrac{110}{12987}}}{\dfrac{911171}{50778}}\\&=&\left(-7\right)\times\dfrac{-\dfrac{25974}{55}}{\dfrac{911171}{50778}}\\&=&\left(-7\right)\times\left(-\dfrac{1318907772}{50114405}\right)\\&=&\dfrac{9232354404}{50114405}\\
\end{eqnarray*}