Ataraxy

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Exercice

L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
Si vous regénérez la page (F5) les valeurs seront changées.
La correction se trouve en bas de page.

Exercice

Calculer \[\left(\dfrac{115}{11}-\left(-\dfrac{37}{5}+\dfrac{115}{11}\right)-\dfrac{19}{6}\right)-\dfrac{\dfrac{\dfrac{\dfrac{\left(-\dfrac{71}{6}+3-\dfrac{5}{4}\right)-\dfrac{136}{5}}{\dfrac{136}{5}}}{11-\dfrac{37}{5}+\dfrac{28}{11}+4}}{-\dfrac{67}{6}}}{\dfrac{44}{5}+\dfrac{\dfrac{\dfrac{136}{5}-\dfrac{136}{5}}{-\dfrac{71}{6}+4+11}}{\left(-2\right)\times\dfrac{44}{5}\times\left(-\dfrac{37}{5}\right)}-\dfrac{67}{6}}-\left(-7+\dfrac{\dfrac{\dfrac{44}{5}}{-2}}{11}\right)\]

Cliquer ici pour afficher la solution

Exercice

On a $ X=\left(\dfrac{115}{11}-\left(-\dfrac{37}{5}+\dfrac{115}{11}\right)-\dfrac{19}{6}\right)-\dfrac{\dfrac{\dfrac{\dfrac{\left(-\dfrac{71}{6}+3-\dfrac{5}{4}\right)-\dfrac{136}{5}}{\dfrac{136}{5}}}{11-\dfrac{37}{5}+\dfrac{28}{11}+4}}{-\dfrac{67}{6}}}{\dfrac{44}{5}+\dfrac{\dfrac{\dfrac{136}{5}-\dfrac{136}{5}}{-\dfrac{71}{6}+4+11}}{\left(-2\right)\times\dfrac{44}{5}\times\left(-\dfrac{37}{5}\right)}-\dfrac{67}{6}}-\left(-7+\dfrac{\dfrac{\dfrac{44}{5}}{-2}}{11}\right)=\dfrac{210073486890}{18049960800}$ . Voici le détail : \begin{eqnarray*} X &=&\left(\dfrac{115}{11}-\left(-\dfrac{37}{5}+\dfrac{115}{11}\right)-\dfrac{19}{6}\right)-\dfrac{\dfrac{\dfrac{\dfrac{\left(-\dfrac{53}{6}-\dfrac{5}{4}\right)-\dfrac{136}{5}}{\dfrac{136}{5}}}{11-\dfrac{37}{5}+\dfrac{28}{11}+4}}{-\dfrac{67}{6}}}{\dfrac{44}{5}+\dfrac{\dfrac{\dfrac{136}{5}-\dfrac{136}{5}}{-\dfrac{71}{6}+4+11}}{\left(-2\right)\times\dfrac{44}{5}\times\left(-\dfrac{37}{5}\right)}-\dfrac{67}{6}}-\left(-7+\dfrac{\dfrac{\dfrac{44}{5}}{-2}}{11}\right)\\&=&\left(\dfrac{115}{11}-\left(-\dfrac{37}{5}+\dfrac{115}{11}\right)-\dfrac{19}{6}\right)-\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{121}{12}-\dfrac{136}{5}}{\dfrac{136}{5}}}{11-\dfrac{37}{5}+\dfrac{28}{11}+4}}{-\dfrac{67}{6}}}{\dfrac{44}{5}+\dfrac{\dfrac{\dfrac{136}{5}-\dfrac{136}{5}}{-\dfrac{71}{6}+4+11}}{\left(-2\right)\times\dfrac{44}{5}\times\left(-\dfrac{37}{5}\right)}-\dfrac{67}{6}}-\left(-7+\dfrac{\dfrac{\dfrac{44}{5}}{-2}}{11}\right)\\&=&\left(\dfrac{115}{11}-\left(-\dfrac{37}{5}+\dfrac{115}{11}\right)-\dfrac{19}{6}\right)-\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{121}{12}-\dfrac{136}{5}}{\dfrac{136}{5}}}{11-\dfrac{267}{55}+4}}{-\dfrac{67}{6}}}{\dfrac{44}{5}+\dfrac{\dfrac{\dfrac{136}{5}-\dfrac{136}{5}}{-\dfrac{71}{6}+4+11}}{\left(-2\right)\times\dfrac{44}{5}\times\left(-\dfrac{37}{5}\right)}-\dfrac{67}{6}}-\left(-7+\dfrac{\dfrac{\dfrac{44}{5}}{-2}}{11}\right)\\&=&\left(\dfrac{115}{11}-\left(-\dfrac{37}{5}+\dfrac{115}{11}\right)-\dfrac{19}{6}\right)-\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{121}{12}-\dfrac{136}{5}}{\dfrac{136}{5}}}{11-\dfrac{47}{55}}}{-\dfrac{67}{6}}}{\dfrac{44}{5}+\dfrac{\dfrac{\dfrac{136}{5}-\dfrac{136}{5}}{-\dfrac{71}{6}+4+11}}{\left(-2\right)\times\dfrac{44}{5}\times\left(-\dfrac{37}{5}\right)}-\dfrac{67}{6}}-\left(-7+\dfrac{\dfrac{\dfrac{44}{5}}{-2}}{11}\right)\\&=&\left(\dfrac{115}{11}-\left(-\dfrac{37}{5}+\dfrac{115}{11}\right)-\dfrac{19}{6}\right)-\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{121}{12}-\dfrac{136}{5}}{\dfrac{136}{5}}}{11-\dfrac{47}{55}}}{-\dfrac{67}{6}}}{\dfrac{44}{5}+\dfrac{\dfrac{0}{-\dfrac{71}{6}+4+11}}{\left(-2\right)\times\dfrac{44}{5}\times\left(-\dfrac{37}{5}\right)}-\dfrac{67}{6}}-\left(-7+\dfrac{\dfrac{\dfrac{44}{5}}{-2}}{11}\right)\\&=&\left(\dfrac{115}{11}-\left(-\dfrac{37}{5}+\dfrac{115}{11}\right)-\dfrac{19}{6}\right)-\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{121}{12}-\dfrac{136}{5}}{\dfrac{136}{5}}}{11-\dfrac{47}{55}}}{-\dfrac{67}{6}}}{\dfrac{44}{5}+\dfrac{\dfrac{0}{-\dfrac{47}{6}+11}}{\left(-2\right)\times\dfrac{44}{5}\times\left(-\dfrac{37}{5}\right)}-\dfrac{67}{6}}-\left(-7+\dfrac{\dfrac{\dfrac{44}{5}}{-2}}{11}\right)\\&=&\left(\dfrac{115}{11}-\left(-\dfrac{37}{5}+\dfrac{115}{11}\right)-\dfrac{19}{6}\right)-\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{121}{12}-\dfrac{136}{5}}{\dfrac{136}{5}}}{11-\dfrac{47}{55}}}{-\dfrac{67}{6}}}{\dfrac{44}{5}+\dfrac{\dfrac{0}{\dfrac{19}{6}}}{\left(-2\right)\times\dfrac{44}{5}\times\left(-\dfrac{37}{5}\right)}-\dfrac{67}{6}}-\left(-7+\dfrac{\dfrac{\dfrac{44}{5}}{-2}}{11}\right)\\&=&\left(\dfrac{115}{11}-\left(-\dfrac{37}{5}+\dfrac{115}{11}\right)-\dfrac{19}{6}\right)-\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{121}{12}-\dfrac{136}{5}}{\dfrac{136}{5}}}{11-\dfrac{47}{55}}}{-\dfrac{67}{6}}}{\dfrac{44}{5}+\dfrac{\dfrac{0}{\dfrac{19}{6}}}{\left(-\dfrac{88}{5}\right)\times\left(-\dfrac{37}{5}\right)}-\dfrac{67}{6}}-\left(-7+\dfrac{\dfrac{\dfrac{44}{5}}{-2}}{11}\right)\\&=&\left(\dfrac{115}{11}-\left(-\dfrac{37}{5}+\dfrac{115}{11}\right)-\dfrac{19}{6}\right)-\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{121}{12}-\dfrac{136}{5}}{\dfrac{136}{5}}}{11-\dfrac{47}{55}}}{-\dfrac{67}{6}}}{\dfrac{44}{5}+\dfrac{\dfrac{0}{\dfrac{19}{6}}}{\dfrac{3256}{25}}-\dfrac{67}{6}}-\left(-7+\dfrac{\dfrac{\dfrac{44}{5}}{-2}}{11}\right)\\&=&\left(\dfrac{115}{11}-\left(-\dfrac{37}{5}+\dfrac{115}{11}\right)-\dfrac{19}{6}\right)-\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{2237}{60}}{\dfrac{136}{5}}}{11-\dfrac{47}{55}}}{-\dfrac{67}{6}}}{\dfrac{44}{5}+\dfrac{\dfrac{0}{\dfrac{19}{6}}}{\dfrac{3256}{25}}-\dfrac{67}{6}}-\left(-7+\dfrac{\dfrac{\dfrac{44}{5}}{-2}}{11}\right)\\&=&\left(\dfrac{115}{11}-\left(-\dfrac{37}{5}+\dfrac{115}{11}\right)-\dfrac{19}{6}\right)-\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{2237}{60}}{\dfrac{136}{5}}}{\dfrac{558}{55}}}{-\dfrac{67}{6}}}{\dfrac{44}{5}+\dfrac{\dfrac{0}{\dfrac{19}{6}}}{\dfrac{3256}{25}}-\dfrac{67}{6}}-\left(-7+\dfrac{\dfrac{\dfrac{44}{5}}{-2}}{11}\right)\\&=&\left(\dfrac{115}{11}-\left(-\dfrac{37}{5}+\dfrac{115}{11}\right)-\dfrac{19}{6}\right)-\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{2237}{60}}{\dfrac{136}{5}}}{\dfrac{558}{55}}}{-\dfrac{67}{6}}}{\dfrac{44}{5}+\dfrac{0}{\dfrac{3256}{25}}-\dfrac{67}{6}}-\left(-7+\dfrac{\dfrac{\dfrac{44}{5}}{-2}}{11}\right)\\&=&\left(\dfrac{115}{11}-\left(-\dfrac{37}{5}+\dfrac{115}{11}\right)-\dfrac{19}{6}\right)-\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{2237}{60}}{\dfrac{136}{5}}}{\dfrac{558}{55}}}{-\dfrac{67}{6}}}{\dfrac{44}{5}+0-\dfrac{67}{6}}-\left(-7+\dfrac{\dfrac{\dfrac{44}{5}}{-2}}{11}\right)\\&=&\left(\dfrac{115}{11}-\dfrac{168}{55}-\dfrac{19}{6}\right)-\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{2237}{60}}{\dfrac{136}{5}}}{\dfrac{558}{55}}}{-\dfrac{67}{6}}}{\dfrac{44}{5}+0-\dfrac{67}{6}}-\left(-7+\dfrac{\dfrac{\dfrac{44}{5}}{-2}}{11}\right)\\&=&\left(\dfrac{115}{11}-\dfrac{168}{55}-\dfrac{19}{6}\right)-\dfrac{\dfrac{\dfrac{-\dfrac{2237}{1632}}{\dfrac{558}{55}}}{-\dfrac{67}{6}}}{\dfrac{44}{5}+0-\dfrac{67}{6}}-\left(-7+\dfrac{\dfrac{\dfrac{44}{5}}{-2}}{11}\right)\\&=&\left(\dfrac{115}{11}-\dfrac{168}{55}-\dfrac{19}{6}\right)-\dfrac{\dfrac{-\dfrac{123035}{910656}}{-\dfrac{67}{6}}}{\dfrac{44}{5}+0-\dfrac{67}{6}}-\left(-7+\dfrac{\dfrac{\dfrac{44}{5}}{-2}}{11}\right)\\&=&\left(\dfrac{115}{11}-\dfrac{168}{55}-\dfrac{19}{6}\right)-\dfrac{\dfrac{-\dfrac{123035}{910656}}{-\dfrac{67}{6}}}{\dfrac{44}{5}-\dfrac{67}{6}}-\left(-7+\dfrac{\dfrac{\dfrac{44}{5}}{-2}}{11}\right)\\&=&\left(\dfrac{115}{11}-\dfrac{168}{55}-\dfrac{19}{6}\right)-\dfrac{\dfrac{-\dfrac{123035}{910656}}{-\dfrac{67}{6}}}{-\dfrac{71}{30}}-\left(-7+\dfrac{\dfrac{\dfrac{44}{5}}{-2}}{11}\right)\\&=&\left(\dfrac{115}{11}-\dfrac{168}{55}-\dfrac{19}{6}\right)-\dfrac{\dfrac{-\dfrac{123035}{910656}}{-\dfrac{67}{6}}}{-\dfrac{71}{30}}-\left(-7+\dfrac{-\dfrac{22}{5}}{11}\right)\\&=&\left(\dfrac{115}{11}-\dfrac{168}{55}-\dfrac{19}{6}\right)-\dfrac{\dfrac{-\dfrac{123035}{910656}}{-\dfrac{67}{6}}}{-\dfrac{71}{30}}-\left(-7-\dfrac{2}{5}\right)\\&=&\left(\dfrac{37}{5}-\dfrac{19}{6}\right)-\dfrac{\dfrac{-\dfrac{123035}{910656}}{-\dfrac{67}{6}}}{-\dfrac{71}{30}}-\left(-7-\dfrac{2}{5}\right)\\&=&\dfrac{127}{30}-\dfrac{\dfrac{-\dfrac{123035}{910656}}{-\dfrac{67}{6}}}{-\dfrac{71}{30}}-\left(-7-\dfrac{2}{5}\right)\\&=&\dfrac{127}{30}-\dfrac{\dfrac{123035}{10168992}}{-\dfrac{71}{30}}-\left(-7-\dfrac{2}{5}\right)\\&=&\dfrac{127}{30}+\dfrac{615175}{120333072}-\left(-7-\dfrac{2}{5}\right)\\&=&\dfrac{127}{30}+\dfrac{615175}{120333072}+\dfrac{37}{5}\\&=&\dfrac{15300755394}{3609992160}+\dfrac{37}{5}\\&=&\dfrac{210073486890}{18049960800}\\ \end{eqnarray*}