L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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Exercice
Calculer \[\left(\left(1-\dfrac{65}{12}+6\right)-\left(6\times\left(-2\right)\times\dfrac{32}{3}-\dfrac{3}{5}\right)\times\dfrac{\dfrac{-\dfrac{65}{12}}{-\dfrac{6}{11}}}{9}\times\left(\dfrac{32}{3}-8+9\right)-\dfrac{133}{8}\right)\times\left(-\dfrac{92}{7}\right)\]
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Exercice
On a \( X=\left(\left(1-\dfrac{65}{12}+6\right)-\left(6\times\left(-2\right)\times\dfrac{32}{3}-\dfrac{3}{5}\right)\times\dfrac{\dfrac{-\dfrac{65}{12}}{-\dfrac{6}{11}}}{9}\times\left(\dfrac{32}{3}-8+9\right)-\dfrac{133}{8}\right)\times\left(-\dfrac{92}{7}\right)=-\dfrac{36673201}{1701}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(\left(1-\dfrac{65}{12}+6\right)-\left(\left(-12\right)\times\dfrac{32}{3}-\dfrac{3}{5}\right)\times\dfrac{\dfrac{-\dfrac{65}{12}}{-\dfrac{6}{11}}}{9}\times\left(\dfrac{32}{3}-8+9\right)-\dfrac{133}{8}\right)\times\left(-\dfrac{92}{7}\right)\\&=&\left(\left(1-\dfrac{65}{12}+6\right)-\left(-128-\dfrac{3}{5}\right)\times\dfrac{\dfrac{-\dfrac{65}{12}}{-\dfrac{6}{11}}}{9}\times\left(\dfrac{32}{3}-8+9\right)-\dfrac{133}{8}\right)\times\left(-\dfrac{92}{7}\right)\\&=&\left(\left(1-\dfrac{65}{12}+6\right)+\dfrac{643}{5}\times\dfrac{\dfrac{-\dfrac{65}{12}}{-\dfrac{6}{11}}}{9}\times\left(\dfrac{32}{3}-8+9\right)-\dfrac{133}{8}\right)\times\left(-\dfrac{92}{7}\right)\\&=&\left(\left(1-\dfrac{65}{12}+6\right)+\dfrac{643}{5}\times\dfrac{\dfrac{715}{72}}{9}\times\left(\dfrac{32}{3}-8+9\right)-\dfrac{133}{8}\right)\times\left(-\dfrac{92}{7}\right)\\&=&\left(\left(1-\dfrac{65}{12}+6\right)+\dfrac{643}{5}\times\dfrac{715}{648}\times\left(\dfrac{32}{3}-8+9\right)-\dfrac{133}{8}\right)\times\left(-\dfrac{92}{7}\right)\\&=&\left(\left(1-\dfrac{65}{12}+6\right)+\dfrac{643}{5}\times\dfrac{715}{648}\times\left(\dfrac{8}{3}+9\right)-\dfrac{133}{8}\right)\times\left(-\dfrac{92}{7}\right)\\&=&\left(\left(1-\dfrac{65}{12}+6\right)+\dfrac{643}{5}\times\dfrac{715}{648}\times\dfrac{35}{3}-\dfrac{133}{8}\right)\times\left(-\dfrac{92}{7}\right)\\&=&\left(\left(-\dfrac{53}{12}+6\right)+\dfrac{643}{5}\times\dfrac{715}{648}\times\dfrac{35}{3}-\dfrac{133}{8}\right)\times\left(-\dfrac{92}{7}\right)\\&=&\left(\dfrac{19}{12}+\dfrac{643}{5}\times\dfrac{715}{648}\times\dfrac{35}{3}-\dfrac{133}{8}\right)\times\left(-\dfrac{92}{7}\right)\\&=&\left(\dfrac{19}{12}-\left(-\dfrac{91949}{648}\right)\times\dfrac{35}{3}-\dfrac{133}{8}\right)\times\left(-\dfrac{92}{7}\right)\\&=&\left(\dfrac{19}{12}+\dfrac{3218215}{1944}-\dfrac{133}{8}\right)\times\left(-\dfrac{92}{7}\right)\\&=&\left(\dfrac{3221293}{1944}-\dfrac{133}{8}\right)\times\left(-\dfrac{92}{7}\right)\\&=&\dfrac{1594487}{972}\times\left(-\dfrac{92}{7}\right)\\&=&-\dfrac{36673201}{1701}\\
\end{eqnarray*}