L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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Exercice
Calculer \[\left(-3\right)\times\dfrac{\dfrac{-\dfrac{87}{8}}{\left(-2+1+\dfrac{92}{9}\right)+12}}{\left(\dfrac{82}{3}-\dfrac{141}{2}\right)\times\left(-2\right)}\times\dfrac{\dfrac{2}{-2}}{2-\dfrac{82}{3}-\dfrac{126}{11}}\times\left(-\dfrac{141}{2}\right)\]
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Exercice
On a \( X=\left(-3\right)\times\dfrac{\dfrac{-\dfrac{87}{8}}{\left(-2+1+\dfrac{92}{9}\right)+12}}{\left(\dfrac{82}{3}-\dfrac{141}{2}\right)\times\left(-2\right)}\times\dfrac{\dfrac{2}{-2}}{2-\dfrac{82}{3}-\dfrac{126}{11}}\times\left(-\dfrac{141}{2}\right)=-\dfrac{32789691}{960885856}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(-3\right)\times\dfrac{\dfrac{-\dfrac{87}{8}}{\left(-1+\dfrac{92}{9}\right)+12}}{\left(\dfrac{82}{3}-\dfrac{141}{2}\right)\times\left(-2\right)}\times\dfrac{\dfrac{2}{-2}}{2-\dfrac{82}{3}-\dfrac{126}{11}}\times\left(-\dfrac{141}{2}\right)\\&=&\left(-3\right)\times\dfrac{\dfrac{-\dfrac{87}{8}}{\dfrac{83}{9}+12}}{\left(\dfrac{82}{3}-\dfrac{141}{2}\right)\times\left(-2\right)}\times\dfrac{\dfrac{2}{-2}}{2-\dfrac{82}{3}-\dfrac{126}{11}}\times\left(-\dfrac{141}{2}\right)\\&=&\left(-3\right)\times\dfrac{\dfrac{-\dfrac{87}{8}}{\dfrac{83}{9}+12}}{-\dfrac{259}{6}\times\left(-2\right)}\times\dfrac{\dfrac{2}{-2}}{2-\dfrac{82}{3}-\dfrac{126}{11}}\times\left(-\dfrac{141}{2}\right)\\&=&\left(-3\right)\times\dfrac{\dfrac{-\dfrac{87}{8}}{\dfrac{83}{9}+12}}{-\dfrac{259}{6}\times\left(-2\right)}\times\dfrac{\dfrac{2}{-2}}{-\dfrac{76}{3}-\dfrac{126}{11}}\times\left(-\dfrac{141}{2}\right)\\&=&\left(-3\right)\times\dfrac{\dfrac{-\dfrac{87}{8}}{\dfrac{191}{9}}}{-\dfrac{259}{6}\times\left(-2\right)}\times\dfrac{\dfrac{2}{-2}}{-\dfrac{76}{3}-\dfrac{126}{11}}\times\left(-\dfrac{141}{2}\right)\\&=&\left(-3\right)\times\dfrac{\dfrac{-\dfrac{87}{8}}{\dfrac{191}{9}}}{\dfrac{259}{3}}\times\dfrac{\dfrac{2}{-2}}{-\dfrac{76}{3}-\dfrac{126}{11}}\times\left(-\dfrac{141}{2}\right)\\&=&\left(-3\right)\times\dfrac{\dfrac{-\dfrac{87}{8}}{\dfrac{191}{9}}}{\dfrac{259}{3}}\times\dfrac{\dfrac{2}{-2}}{-\dfrac{1214}{33}}\times\left(-\dfrac{141}{2}\right)\\&=&\left(-3\right)\times\dfrac{-\dfrac{783}{1528}}{\dfrac{259}{3}}\times\dfrac{\dfrac{2}{-2}}{-\dfrac{1214}{33}}\times\left(-\dfrac{141}{2}\right)\\&=&\left(-3\right)\times\left(-\dfrac{2349}{395752}\right)\times\dfrac{\dfrac{2}{-2}}{-\dfrac{1214}{33}}\times\left(-\dfrac{141}{2}\right)\\&=&\left(-3\right)\times\left(-\dfrac{2349}{395752}\right)\times\dfrac{-1}{-\dfrac{1214}{33}}\times\left(-\dfrac{141}{2}\right)\\&=&\left(-3\right)\times\left(-\dfrac{2349}{395752}\right)\times\left(\dfrac{33}{1214}\right)\times\left(-\dfrac{141}{2}\right)\\&=&\left(-3\right)\times-\dfrac{77517}{480442928}\times\left(-\dfrac{141}{2}\right)\\&=&\left(-3\right)\times\left(\dfrac{10929897}{960885856}\right)\\&=&-\dfrac{32789691}{960885856}\\
\end{eqnarray*}