L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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Exercice
Calculer \[\left(-\dfrac{117}{8}+8-\dfrac{\dfrac{-\dfrac{109}{4}}{2}}{\dfrac{107}{4}-\dfrac{34}{11}-3}\times\dfrac{\dfrac{\dfrac{3}{3}}{-8}}{\dfrac{17}{2}+3-\dfrac{117}{8}}\right)-\dfrac{34}{11}+\dfrac{117}{8}\]
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Exercice
On a \( X=\left(-\dfrac{117}{8}+8-\dfrac{\dfrac{-\dfrac{109}{4}}{2}}{\dfrac{107}{4}-\dfrac{34}{11}-3}\times\dfrac{\dfrac{\dfrac{3}{3}}{-8}}{\dfrac{17}{2}+3-\dfrac{117}{8}}\right)-\dfrac{34}{11}+\dfrac{117}{8}=\dfrac{2467489}{499950}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(-\dfrac{117}{8}+8-\dfrac{\dfrac{-\dfrac{109}{4}}{2}}{\dfrac{1041}{44}-3}\times\dfrac{\dfrac{\dfrac{3}{3}}{-8}}{\dfrac{17}{2}+3-\dfrac{117}{8}}\right)-\dfrac{34}{11}+\dfrac{117}{8}\\&=&\left(-\dfrac{117}{8}+8-\dfrac{\dfrac{-\dfrac{109}{4}}{2}}{\dfrac{909}{44}}\times\dfrac{\dfrac{\dfrac{3}{3}}{-8}}{\dfrac{17}{2}+3-\dfrac{117}{8}}\right)-\dfrac{34}{11}+\dfrac{117}{8}\\&=&\left(-\dfrac{117}{8}+8-\dfrac{\dfrac{-\dfrac{109}{4}}{2}}{\dfrac{909}{44}}\times\dfrac{\dfrac{1}{-8}}{\dfrac{17}{2}+3-\dfrac{117}{8}}\right)-\dfrac{34}{11}+\dfrac{117}{8}\\&=&\left(-\dfrac{117}{8}+8-\dfrac{\dfrac{-\dfrac{109}{4}}{2}}{\dfrac{909}{44}}\times\dfrac{-\dfrac{1}{8}}{\dfrac{17}{2}+3-\dfrac{117}{8}}\right)-\dfrac{34}{11}+\dfrac{117}{8}\\&=&\left(-\dfrac{117}{8}+8-\dfrac{\dfrac{-\dfrac{109}{4}}{2}}{\dfrac{909}{44}}\times\dfrac{-\dfrac{1}{8}}{\dfrac{23}{2}-\dfrac{117}{8}}\right)-\dfrac{34}{11}+\dfrac{117}{8}\\&=&\left(-\dfrac{117}{8}+8-\dfrac{\dfrac{-\dfrac{109}{4}}{2}}{\dfrac{909}{44}}\times\dfrac{-\dfrac{1}{8}}{-\dfrac{25}{8}}\right)-\dfrac{34}{11}+\dfrac{117}{8}\\&=&\left(-\dfrac{117}{8}+8-\dfrac{-\dfrac{109}{8}}{\dfrac{909}{44}}\times\dfrac{-\dfrac{1}{8}}{-\dfrac{25}{8}}\right)-\dfrac{34}{11}+\dfrac{117}{8}\\&=&\left(-\dfrac{117}{8}+8-\left(-\dfrac{1199}{1818}\right)\times\dfrac{-\dfrac{1}{8}}{-\dfrac{25}{8}}\right)-\dfrac{34}{11}+\dfrac{117}{8}\\&=&\left(-\dfrac{117}{8}+8-\left(-\dfrac{1199}{1818}\right)\times\dfrac{1}{25}\right)-\dfrac{34}{11}+\dfrac{117}{8}\\&=&\left(-\dfrac{117}{8}+8+\dfrac{1199}{45450}\right)-\dfrac{34}{11}+\dfrac{117}{8}\\&=&\left(-\dfrac{53}{8}+\dfrac{1199}{45450}\right)-\dfrac{34}{11}+\dfrac{117}{8}\\&=&-\dfrac{1199629}{181800}-\dfrac{34}{11}+\dfrac{117}{8}\\&=&-\dfrac{19377119}{1999800}+\dfrac{117}{8}\\&=&\dfrac{2467489}{499950}\\
\end{eqnarray*}