L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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Exercice
Calculer \[\left(-\dfrac{95}{7}\right)\times\left(\dfrac{61}{8}+\dfrac{\dfrac{\dfrac{38}{3}}{11}}{9}+\dfrac{95}{3}+\left(\dfrac{95}{3}-\dfrac{137}{9}\right)-\dfrac{\dfrac{\dfrac{-5}{-4}}{\dfrac{137}{9}}}{\dfrac{137}{9}}-\dfrac{\dfrac{\dfrac{-\dfrac{72}{5}}{8}}{\dfrac{38}{3}}}{\dfrac{137}{9}}-\left(\dfrac{38}{3}-9+5\right)-\dfrac{95}{7}\right)\times9\]
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Exercice
On a \( X=\left(-\dfrac{95}{7}\right)\times\left(\dfrac{61}{8}+\dfrac{\dfrac{\dfrac{38}{3}}{11}}{9}+\dfrac{95}{3}+\left(\dfrac{95}{3}-\dfrac{137}{9}\right)-\dfrac{\dfrac{\dfrac{-5}{-4}}{\dfrac{137}{9}}}{\dfrac{137}{9}}-\dfrac{\dfrac{\dfrac{-\dfrac{72}{5}}{8}}{\dfrac{38}{3}}}{\dfrac{137}{9}}-\left(\dfrac{38}{3}-9+5\right)-\dfrac{95}{7}\right)\times9=-\dfrac{7.5700111015957E+19}{18429044934928320}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(-\dfrac{95}{7}\right)\times\left(\dfrac{61}{8}+\dfrac{\dfrac{\dfrac{38}{3}}{11}}{9}+\dfrac{95}{3}+\dfrac{148}{9}-\dfrac{\dfrac{\dfrac{-5}{-4}}{\dfrac{137}{9}}}{\dfrac{137}{9}}-\dfrac{\dfrac{\dfrac{-\dfrac{72}{5}}{8}}{\dfrac{38}{3}}}{\dfrac{137}{9}}-\left(\dfrac{38}{3}-9+5\right)-\dfrac{95}{7}\right)\times9\\&=&\left(-\dfrac{95}{7}\right)\times\left(\dfrac{61}{8}+\dfrac{\dfrac{\dfrac{38}{3}}{11}}{9}+\dfrac{95}{3}+\dfrac{148}{9}-\dfrac{\dfrac{\dfrac{5}{4}}{\dfrac{137}{9}}}{\dfrac{137}{9}}-\dfrac{\dfrac{\dfrac{-\dfrac{72}{5}}{8}}{\dfrac{38}{3}}}{\dfrac{137}{9}}-\left(\dfrac{38}{3}-9+5\right)-\dfrac{95}{7}\right)\times9\\&=&\left(-\dfrac{95}{7}\right)\times\left(\dfrac{61}{8}+\dfrac{\dfrac{\dfrac{38}{3}}{11}}{9}+\dfrac{95}{3}+\dfrac{148}{9}-\dfrac{\dfrac{45}{548}}{\dfrac{137}{9}}-\dfrac{\dfrac{\dfrac{-\dfrac{72}{5}}{8}}{\dfrac{38}{3}}}{\dfrac{137}{9}}-\left(\dfrac{38}{3}-9+5\right)-\dfrac{95}{7}\right)\times9\\&=&\left(-\dfrac{95}{7}\right)\times\left(\dfrac{61}{8}+\dfrac{\dfrac{\dfrac{38}{3}}{11}}{9}+\dfrac{95}{3}+\dfrac{148}{9}-\dfrac{405}{75076}-\dfrac{\dfrac{\dfrac{-\dfrac{72}{5}}{8}}{\dfrac{38}{3}}}{\dfrac{137}{9}}-\left(\dfrac{38}{3}-9+5\right)-\dfrac{95}{7}\right)\times9\\&=&\left(-\dfrac{95}{7}\right)\times\left(\dfrac{61}{8}+\dfrac{\dfrac{\dfrac{38}{3}}{11}}{9}+\dfrac{95}{3}+\dfrac{148}{9}-\dfrac{405}{75076}-\dfrac{\dfrac{-\dfrac{9}{5}}{\dfrac{38}{3}}}{\dfrac{137}{9}}-\left(\dfrac{38}{3}-9+5\right)-\dfrac{95}{7}\right)\times9\\&=&\left(-\dfrac{95}{7}\right)\times\left(\dfrac{61}{8}+\dfrac{\dfrac{\dfrac{38}{3}}{11}}{9}+\dfrac{95}{3}+\dfrac{148}{9}-\dfrac{405}{75076}-\dfrac{-\dfrac{27}{190}}{\dfrac{137}{9}}-\left(\dfrac{38}{3}-9+5\right)-\dfrac{95}{7}\right)\times9\\&=&\left(-\dfrac{95}{7}\right)\times\left(\dfrac{61}{8}+\dfrac{\dfrac{\dfrac{38}{3}}{11}}{9}+\dfrac{95}{3}+\dfrac{148}{9}-\dfrac{405}{75076}+\dfrac{243}{26030}-\left(\dfrac{38}{3}-9+5\right)-\dfrac{95}{7}\right)\times9\\&=&\left(-\dfrac{95}{7}\right)\times\left(\dfrac{61}{8}+\dfrac{\dfrac{\dfrac{38}{3}}{11}}{9}+\dfrac{95}{3}+\dfrac{148}{9}-\dfrac{405}{75076}+\dfrac{243}{26030}-\left(\dfrac{11}{3}+5\right)-\dfrac{95}{7}\right)\times9\\&=&\left(-\dfrac{95}{7}\right)\times\left(\dfrac{61}{8}+\dfrac{\dfrac{\dfrac{38}{3}}{11}}{9}+\dfrac{95}{3}+\dfrac{148}{9}-\dfrac{405}{75076}+\dfrac{243}{26030}-\dfrac{26}{3}-\dfrac{95}{7}\right)\times9\\&=&\left(-\dfrac{95}{7}\right)\times\left(\dfrac{61}{8}+\dfrac{\dfrac{\dfrac{38}{3}}{11}}{9}+\dfrac{95}{3}+\dfrac{11107603}{675684}+\dfrac{243}{26030}-\dfrac{26}{3}-\dfrac{95}{7}\right)\times9\\&=&\left(-\dfrac{95}{7}\right)\times\left(\dfrac{61}{8}+\dfrac{\dfrac{\dfrac{38}{3}}{11}}{9}+\dfrac{95}{3}+\dfrac{289295097302}{17588054520}-\dfrac{26}{3}-\dfrac{95}{7}\right)\times9\\&=&\left(-\dfrac{95}{7}\right)\times\left(\dfrac{61}{8}+\dfrac{\dfrac{\dfrac{38}{3}}{11}}{9}+\dfrac{95}{3}+\dfrac{410595874386}{52764163560}-\dfrac{95}{7}\right)\times9\\&=&\left(-\dfrac{95}{7}\right)\times\left(\dfrac{61}{8}+\dfrac{\dfrac{38}{33}}{9}+\dfrac{95}{3}+\dfrac{410595874386}{52764163560}-\dfrac{95}{7}\right)\times9\\&=&\left(-\dfrac{95}{7}\right)\times\left(\dfrac{61}{8}+\dfrac{38}{297}+\dfrac{95}{3}+\dfrac{410595874386}{52764163560}-\dfrac{95}{7}\right)\times9\\&=&\left(-\dfrac{95}{7}\right)\times\left(\dfrac{61}{8}+\dfrac{38}{297}+\dfrac{6244383161358}{158292490680}-\dfrac{95}{7}\right)\times9\\&=&\left(-\dfrac{95}{7}\right)\times\left(\dfrac{61}{8}+\dfrac{38}{297}+\dfrac{28672895514906}{1108047434760}\right)\times9\\&=&\left(-\dfrac{95}{7}\right)\times\left(\dfrac{18421}{2376}+\dfrac{28672895514906}{1108047434760}\right)\times9\\&=&\left(-\dfrac{95}{7}\right)\times\dfrac{88538141539130616}{2632720704989760}\times9\\&=&\left(-\dfrac{8411123446217408520}{18429044934928320}\right)\times9\\&=&-\dfrac{7.5700111015957E+19}{18429044934928320}\\
\end{eqnarray*}