L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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Exercice
Calculer \[\dfrac{96}{5}\times6\times\left(-12\right)\times6+7+12-\left(\left(4+12\right)\times\left(\dfrac{96}{5}-\left(-12\right)\times3\times\dfrac{37}{3}-\left(0+7+7+\dfrac{57}{4}\right)\right)\times\left(\dfrac{\dfrac{-2}{3}}{-\dfrac{59}{6}}-12\right)\times\left(-7\right)-12+\dfrac{37}{3}-\left(4+\dfrac{37}{3}+0+4\right)\right)\]
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Exercice
On a \( X=\dfrac{96}{5}\times6\times\left(-12\right)\times6+7+12-\left(\left(4+12\right)\times\left(\dfrac{96}{5}-\left(-12\right)\times3\times\dfrac{37}{3}-\left(0+7+7+\dfrac{57}{4}\right)\right)\times\left(\dfrac{\dfrac{-2}{3}}{-\dfrac{59}{6}}-12\right)\times\left(-7\right)-12+\dfrac{37}{3}-\left(4+\dfrac{37}{3}+0+4\right)\right)=-\dfrac{173910031}{295}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{96}{5}\times6\times\left(-12\right)\times6+7+12-\left(\left(4+12\right)\times\left(\dfrac{96}{5}-\left(-36\right)\times\dfrac{37}{3}-\left(0+7+7+\dfrac{57}{4}\right)\right)\times\left(\dfrac{\dfrac{-2}{3}}{-\dfrac{59}{6}}-12\right)\times\left(-7\right)-12+\dfrac{37}{3}-\left(4+\dfrac{37}{3}+0+4\right)\right)\\&=&\dfrac{96}{5}\times6\times\left(-12\right)\times6+7+12-\left(\left(4+12\right)\times\left(\dfrac{96}{5}+444-\left(0+7+7+\dfrac{57}{4}\right)\right)\times\left(\dfrac{\dfrac{-2}{3}}{-\dfrac{59}{6}}-12\right)\times\left(-7\right)-12+\dfrac{37}{3}-\left(4+\dfrac{37}{3}+0+4\right)\right)\\&=&\dfrac{96}{5}\times6\times\left(-12\right)\times6+7+12-\left(\left(4+12\right)\times\left(\dfrac{96}{5}+444-\left(7+7+\dfrac{57}{4}\right)\right)\times\left(\dfrac{\dfrac{-2}{3}}{-\dfrac{59}{6}}-12\right)\times\left(-7\right)-12+\dfrac{37}{3}-\left(4+\dfrac{37}{3}+0+4\right)\right)\\&=&\dfrac{96}{5}\times6\times\left(-12\right)\times6+7+12-\left(\left(4+12\right)\times\left(\dfrac{96}{5}+444-\left(14+\dfrac{57}{4}\right)\right)\times\left(\dfrac{\dfrac{-2}{3}}{-\dfrac{59}{6}}-12\right)\times\left(-7\right)-12+\dfrac{37}{3}-\left(4+\dfrac{37}{3}+0+4\right)\right)\\&=&\dfrac{96}{5}\times6\times\left(-12\right)\times6+7+12-\left(\left(4+12\right)\times\left(\dfrac{96}{5}+444-\dfrac{113}{4}\right)\times\left(\dfrac{\dfrac{-2}{3}}{-\dfrac{59}{6}}-12\right)\times\left(-7\right)-12+\dfrac{37}{3}-\left(4+\dfrac{37}{3}+0+4\right)\right)\\&=&\dfrac{96}{5}\times6\times\left(-12\right)\times6+7+12-\left(\left(4+12\right)\times\left(\dfrac{96}{5}+444-\dfrac{113}{4}\right)\times\left(\dfrac{-\dfrac{2}{3}}{-\dfrac{59}{6}}-12\right)\times\left(-7\right)-12+\dfrac{37}{3}-\left(4+\dfrac{37}{3}+0+4\right)\right)\\&=&\dfrac{96}{5}\times6\times\left(-12\right)\times6+7+12-\left(\left(4+12\right)\times\left(\dfrac{96}{5}+444-\dfrac{113}{4}\right)\times\left(\dfrac{4}{59}-12\right)\times\left(-7\right)-12+\dfrac{37}{3}-\left(4+\dfrac{37}{3}+0+4\right)\right)\\&=&\dfrac{96}{5}\times6\times\left(-12\right)\times6+7+12-\left(16\times\left(\dfrac{96}{5}+444-\dfrac{113}{4}\right)\times\left(\dfrac{4}{59}-12\right)\times\left(-7\right)-12+\dfrac{37}{3}-\left(4+\dfrac{37}{3}+0+4\right)\right)\\&=&\dfrac{96}{5}\times6\times\left(-12\right)\times6+7+12-\left(16\times\left(\dfrac{2316}{5}-\dfrac{113}{4}\right)\times\left(\dfrac{4}{59}-12\right)\times\left(-7\right)-12+\dfrac{37}{3}-\left(4+\dfrac{37}{3}+0+4\right)\right)\\&=&\dfrac{96}{5}\times6\times\left(-12\right)\times6+7+12-\left(16\times\dfrac{8699}{20}\times\left(\dfrac{4}{59}-12\right)\times\left(-7\right)-12+\dfrac{37}{3}-\left(4+\dfrac{37}{3}+0+4\right)\right)\\&=&\dfrac{96}{5}\times6\times\left(-12\right)\times6+7+12-\left(16\times\dfrac{8699}{20}\times-\dfrac{704}{59}\times\left(-7\right)-12+\dfrac{37}{3}-\left(4+\dfrac{37}{3}+0+4\right)\right)\\&=&\dfrac{96}{5}\times6\times\left(-12\right)\times6+7+12-\left(16\times\dfrac{8699}{20}\times-\dfrac{704}{59}\times\left(-7\right)-12+\dfrac{37}{3}-\left(\dfrac{49}{3}+0+4\right)\right)\\&=&\dfrac{96}{5}\times6\times\left(-12\right)\times6+7+12-\left(16\times\dfrac{8699}{20}\times-\dfrac{704}{59}\times\left(-7\right)-12+\dfrac{37}{3}-\left(\dfrac{49}{3}+4\right)\right)\\&=&\dfrac{96}{5}\times6\times\left(-12\right)\times6+7+12-\left(16\times\dfrac{8699}{20}\times-\dfrac{704}{59}\times\left(-7\right)-12+\dfrac{37}{3}-\dfrac{61}{3}\right)\\&=&\dfrac{96}{5}\times6\times\left(-12\right)\times6+7+12-\left(\dfrac{34796}{5}\times-\dfrac{704}{59}\times\left(-7\right)-12+\dfrac{37}{3}-\dfrac{61}{3}\right)\\&=&\dfrac{96}{5}\times6\times\left(-12\right)\times6+7+12-\left(-\dfrac{24496384}{295}\times\left(-7\right)-12+\dfrac{37}{3}-\dfrac{61}{3}\right)\\&=&\dfrac{96}{5}\times6\times\left(-12\right)\times6+7+12-\left(\dfrac{171474688}{295}-12+\dfrac{37}{3}-\dfrac{61}{3}\right)\\&=&\dfrac{96}{5}\times6\times\left(-12\right)\times6+7+12-\left(\dfrac{171474688}{295}-12-8\right)\\&=&\dfrac{576}{5}\times\left(-12\right)\times6+7+12-\left(\dfrac{171474688}{295}-12-8\right)\\&=&\left(-\dfrac{6912}{5}\right)\times6+7+12-\left(\dfrac{171474688}{295}-12-8\right)\\&=&-\dfrac{41472}{5}+7+12-\left(\dfrac{171474688}{295}-12-8\right)\\&=&-\dfrac{41472}{5}+7+12-\left(\dfrac{171471148}{295}-8\right)\\&=&-\dfrac{41472}{5}+7+12-\dfrac{171468788}{295}\\&=&-\dfrac{41437}{5}+12-\dfrac{171468788}{295}\\&=&-\dfrac{41377}{5}-\dfrac{171468788}{295}\\&=&-\dfrac{173910031}{295}\\
\end{eqnarray*}