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 \[\dfrac{\dfrac{-3}{\left(-3\right)\times\left(-11\right)}}{12}\times\left(-11\right)\times\left(-3-\dfrac{98}{3}+\dfrac{\dfrac{-\dfrac{17}{2}}{-\dfrac{17}{2}}}{\left(-\dfrac{17}{2}\right)\times\left(-3\right)\times\dfrac{54}{11}}\right)-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{\dfrac{\dfrac{-\dfrac{17}{2}}{-11}}{-12}}-\left(\left(-3\right)\times\dfrac{\dfrac{\dfrac{-3}{-3}}{-\dfrac{24}{5}}}{12}-\left(\left(-3+\left(-11\right)\times\dfrac{122}{3}\times\dfrac{122}{3}\right)+\dfrac{76}{5}\right)-\left(-3-12\right)\times\left(-11-\dfrac{98}{3}\right)\right)\]

Cliquer ici pour afficher la solution

Exercice

On a $ X=\dfrac{\dfrac{-3}{\left(-3\right)\times\left(-11\right)}}{12}\times\left(-11\right)\times\left(-3-\dfrac{98}{3}+\dfrac{\dfrac{-\dfrac{17}{2}}{-\dfrac{17}{2}}}{\left(-\dfrac{17}{2}\right)\times\left(-3\right)\times\dfrac{54}{11}}\right)-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{\dfrac{\dfrac{-\dfrac{17}{2}}{-11}}{-12}}-\left(\left(-3\right)\times\dfrac{\dfrac{\dfrac{-3}{-3}}{-\dfrac{24}{5}}}{12}-\left(\left(-3+\left(-11\right)\times\dfrac{122}{3}\times\dfrac{122}{3}\right)+\dfrac{76}{5}\right)-\left(-3-12\right)\times\left(-11-\dfrac{98}{3}\right)\right)=-\dfrac{30159351259650}{1725105600}$ . Voici le détail : \begin{eqnarray*} X &=&\dfrac{\dfrac{-3}{\left(-3\right)\times\left(-11\right)}}{12}\times\left(-11\right)\times\left(-3-\dfrac{98}{3}+\dfrac{\dfrac{-\dfrac{17}{2}}{-\dfrac{17}{2}}}{\dfrac{51}{2}\times\dfrac{54}{11}}\right)-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{\dfrac{\dfrac{-\dfrac{17}{2}}{-11}}{-12}}-\left(\left(-3\right)\times\dfrac{\dfrac{\dfrac{-3}{-3}}{-\dfrac{24}{5}}}{12}-\left(\left(-3+\left(-11\right)\times\dfrac{122}{3}\times\dfrac{122}{3}\right)+\dfrac{76}{5}\right)-\left(-3-12\right)\times\left(-11-\dfrac{98}{3}\right)\right)\\&=&\dfrac{\dfrac{-3}{\left(-3\right)\times\left(-11\right)}}{12}\times\left(-11\right)\times\left(-3-\dfrac{98}{3}+\dfrac{\dfrac{-\dfrac{17}{2}}{-\dfrac{17}{2}}}{\dfrac{1377}{11}}\right)-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{\dfrac{\dfrac{-\dfrac{17}{2}}{-11}}{-12}}-\left(\left(-3\right)\times\dfrac{\dfrac{\dfrac{-3}{-3}}{-\dfrac{24}{5}}}{12}-\left(\left(-3+\left(-11\right)\times\dfrac{122}{3}\times\dfrac{122}{3}\right)+\dfrac{76}{5}\right)-\left(-3-12\right)\times\left(-11-\dfrac{98}{3}\right)\right)\\&=&\dfrac{\dfrac{-3}{\left(-3\right)\times\left(-11\right)}}{12}\times\left(-11\right)\times\left(-3-\dfrac{98}{3}+\dfrac{\dfrac{-\dfrac{17}{2}}{-\dfrac{17}{2}}}{\dfrac{1377}{11}}\right)-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{\dfrac{\dfrac{-\dfrac{17}{2}}{-11}}{-12}}-\left(\left(-3\right)\times\dfrac{\dfrac{1}{-\dfrac{24}{5}}}{12}-\left(\left(-3+\left(-11\right)\times\dfrac{122}{3}\times\dfrac{122}{3}\right)+\dfrac{76}{5}\right)-\left(-3-12\right)\times\left(-11-\dfrac{98}{3}\right)\right)\\&=&\dfrac{\dfrac{-3}{\left(-3\right)\times\left(-11\right)}}{12}\times\left(-11\right)\times\left(-3-\dfrac{98}{3}+\dfrac{\dfrac{-\dfrac{17}{2}}{-\dfrac{17}{2}}}{\dfrac{1377}{11}}\right)-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{\dfrac{\dfrac{-\dfrac{17}{2}}{-11}}{-12}}-\left(\left(-3\right)\times\dfrac{\dfrac{1}{-\dfrac{24}{5}}}{12}-\left(\left(-3+\left(-\dfrac{1342}{3}\right)\times\dfrac{122}{3}\right)+\dfrac{76}{5}\right)-\left(-3-12\right)\times\left(-11-\dfrac{98}{3}\right)\right)\\&=&\dfrac{\dfrac{-3}{\left(-3\right)\times\left(-11\right)}}{12}\times\left(-11\right)\times\left(-3-\dfrac{98}{3}+\dfrac{\dfrac{-\dfrac{17}{2}}{-\dfrac{17}{2}}}{\dfrac{1377}{11}}\right)-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{\dfrac{\dfrac{-\dfrac{17}{2}}{-11}}{-12}}-\left(\left(-3\right)\times\dfrac{\dfrac{1}{-\dfrac{24}{5}}}{12}-\left(\left(-3-\dfrac{163724}{9}\right)+\dfrac{76}{5}\right)-\left(-3-12\right)\times\left(-11-\dfrac{98}{3}\right)\right)\\&=&\dfrac{\dfrac{-3}{33}}{12}\times\left(-11\right)\times\left(-3-\dfrac{98}{3}+\dfrac{\dfrac{-\dfrac{17}{2}}{-\dfrac{17}{2}}}{\dfrac{1377}{11}}\right)-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{\dfrac{\dfrac{-\dfrac{17}{2}}{-11}}{-12}}-\left(\left(-3\right)\times\dfrac{\dfrac{1}{-\dfrac{24}{5}}}{12}-\left(\left(-3-\dfrac{163724}{9}\right)+\dfrac{76}{5}\right)-\left(-3-12\right)\times\left(-11-\dfrac{98}{3}\right)\right)\\&=&\dfrac{\dfrac{-3}{33}}{12}\times\left(-11\right)\times\left(-\dfrac{107}{3}+\dfrac{\dfrac{-\dfrac{17}{2}}{-\dfrac{17}{2}}}{\dfrac{1377}{11}}\right)-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{\dfrac{\dfrac{-\dfrac{17}{2}}{-11}}{-12}}-\left(\left(-3\right)\times\dfrac{\dfrac{1}{-\dfrac{24}{5}}}{12}-\left(\left(-3-\dfrac{163724}{9}\right)+\dfrac{76}{5}\right)-\left(-3-12\right)\times\left(-11-\dfrac{98}{3}\right)\right)\\&=&\dfrac{\dfrac{-3}{33}}{12}\times\left(-11\right)\times\left(-\dfrac{107}{3}+\dfrac{1}{\dfrac{1377}{11}}\right)-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{\dfrac{\dfrac{-\dfrac{17}{2}}{-11}}{-12}}-\left(\left(-3\right)\times\dfrac{\dfrac{1}{-\dfrac{24}{5}}}{12}-\left(\left(-3-\dfrac{163724}{9}\right)+\dfrac{76}{5}\right)-\left(-3-12\right)\times\left(-11-\dfrac{98}{3}\right)\right)\\&=&\dfrac{\dfrac{-3}{33}}{12}\times\left(-11\right)\times\left(-\dfrac{107}{3}+\dfrac{11}{1377}\right)-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{\dfrac{\dfrac{-\dfrac{17}{2}}{-11}}{-12}}-\left(\left(-3\right)\times\dfrac{\dfrac{1}{-\dfrac{24}{5}}}{12}-\left(\left(-3-\dfrac{163724}{9}\right)+\dfrac{76}{5}\right)-\left(-3-12\right)\times\left(-11-\dfrac{98}{3}\right)\right)\\&=&\dfrac{\dfrac{-3}{33}}{12}\times\left(-11\right)\times\left(-\dfrac{107}{3}+\dfrac{11}{1377}\right)-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{\dfrac{\dfrac{-\dfrac{17}{2}}{-11}}{-12}}-\left(\left(-3\right)\times\dfrac{-\dfrac{5}{24}}{12}-\left(\left(-3-\dfrac{163724}{9}\right)+\dfrac{76}{5}\right)-\left(-3-12\right)\times\left(-11-\dfrac{98}{3}\right)\right)\\&=&\dfrac{\dfrac{-3}{33}}{12}\times\left(-11\right)\times\left(-\dfrac{107}{3}+\dfrac{11}{1377}\right)-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{\dfrac{\dfrac{-\dfrac{17}{2}}{-11}}{-12}}-\left(\left(-3\right)\times\left(-\dfrac{5}{288}\right)-\left(\left(-3-\dfrac{163724}{9}\right)+\dfrac{76}{5}\right)-\left(-3-12\right)\times\left(-11-\dfrac{98}{3}\right)\right)\\&=&\dfrac{\dfrac{-3}{33}}{12}\times\left(-11\right)\times\left(-\dfrac{107}{3}+\dfrac{11}{1377}\right)-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{\dfrac{\dfrac{-\dfrac{17}{2}}{-11}}{-12}}-\left(\left(-3\right)\times\left(-\dfrac{5}{288}\right)-\left(-\dfrac{163751}{9}+\dfrac{76}{5}\right)-\left(-3-12\right)\times\left(-11-\dfrac{98}{3}\right)\right)\\&=&\dfrac{\dfrac{-3}{33}}{12}\times\left(-11\right)\times\left(-\dfrac{107}{3}+\dfrac{11}{1377}\right)-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{\dfrac{\dfrac{-\dfrac{17}{2}}{-11}}{-12}}-\left(\left(-3\right)\times\left(-\dfrac{5}{288}\right)-\left(-\dfrac{163751}{9}+\dfrac{76}{5}\right)+15\times\left(-11-\dfrac{98}{3}\right)\right)\\&=&\dfrac{\dfrac{-3}{33}}{12}\times\left(-11\right)\times\left(-\dfrac{107}{3}+\dfrac{11}{1377}\right)-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{\dfrac{\dfrac{-\dfrac{17}{2}}{-11}}{-12}}-\left(\left(-3\right)\times\left(-\dfrac{5}{288}\right)-\left(-\dfrac{163751}{9}+\dfrac{76}{5}\right)+15\times-\dfrac{131}{3}\right)\\&=&\dfrac{-\dfrac{1}{11}}{12}\times\left(-11\right)\times\left(-\dfrac{107}{3}+\dfrac{11}{1377}\right)-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{\dfrac{\dfrac{-\dfrac{17}{2}}{-11}}{-12}}-\left(\left(-3\right)\times\left(-\dfrac{5}{288}\right)-\left(-\dfrac{163751}{9}+\dfrac{76}{5}\right)+15\times-\dfrac{131}{3}\right)\\&=&\left(-\dfrac{1}{132}\right)\times\left(-11\right)\times\left(-\dfrac{107}{3}+\dfrac{11}{1377}\right)-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{\dfrac{\dfrac{-\dfrac{17}{2}}{-11}}{-12}}-\left(\left(-3\right)\times\left(-\dfrac{5}{288}\right)-\left(-\dfrac{163751}{9}+\dfrac{76}{5}\right)+15\times-\dfrac{131}{3}\right)\\&=&\left(-\dfrac{1}{132}\right)\times\left(-11\right)\times\left(-\dfrac{49102}{1377}\right)-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{\dfrac{\dfrac{-\dfrac{17}{2}}{-11}}{-12}}-\left(\left(-3\right)\times\left(-\dfrac{5}{288}\right)-\left(-\dfrac{163751}{9}+\dfrac{76}{5}\right)+15\times-\dfrac{131}{3}\right)\\&=&\left(-\dfrac{1}{132}\right)\times\left(-11\right)\times\left(-\dfrac{49102}{1377}\right)-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{\dfrac{\dfrac{17}{22}}{-12}}-\left(\left(-3\right)\times\left(-\dfrac{5}{288}\right)-\left(-\dfrac{163751}{9}+\dfrac{76}{5}\right)+15\times-\dfrac{131}{3}\right)\\&=&\left(-\dfrac{1}{132}\right)\times\left(-11\right)\times\left(-\dfrac{49102}{1377}\right)-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{-\dfrac{17}{264}}-\left(\left(-3\right)\times\left(-\dfrac{5}{288}\right)-\left(-\dfrac{163751}{9}+\dfrac{76}{5}\right)+15\times-\dfrac{131}{3}\right)\\&=&\left(-\dfrac{1}{132}\right)\times\left(-11\right)\times\left(-\dfrac{49102}{1377}\right)-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{-\dfrac{17}{264}}-\left(\dfrac{5}{96}-\left(-\dfrac{163751}{9}+\dfrac{76}{5}\right)+15\times-\dfrac{131}{3}\right)\\&=&\left(-\dfrac{1}{132}\right)\times\left(-11\right)\times\left(-\dfrac{49102}{1377}\right)-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{-\dfrac{17}{264}}-\left(\dfrac{5}{96}+\dfrac{818071}{45}+15\times-\dfrac{131}{3}\right)\\&=&\left(-\dfrac{1}{132}\right)\times\left(-11\right)\times\left(-\dfrac{49102}{1377}\right)-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{-\dfrac{17}{264}}-\left(\dfrac{5}{96}+\dfrac{818071}{45}-655\right)\\&=&\dfrac{1}{12}\times\left(-\dfrac{49102}{1377}\right)-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{-\dfrac{17}{264}}-\left(\dfrac{5}{96}+\dfrac{818071}{45}-655\right)\\&=&-\dfrac{24551}{8262}-\dfrac{\dfrac{-\dfrac{76}{5}}{-\dfrac{58}{11}}}{-\dfrac{17}{264}}-\left(\dfrac{5}{96}+\dfrac{818071}{45}-655\right)\\&=&-\dfrac{24551}{8262}-\dfrac{\dfrac{418}{145}}{-\dfrac{17}{264}}-\left(\dfrac{5}{96}+\dfrac{818071}{45}-655\right)\\&=&-\dfrac{24551}{8262}+\dfrac{110352}{2465}-\left(\dfrac{5}{96}+\dfrac{818071}{45}-655\right)\\&=&-\dfrac{24551}{8262}+\dfrac{110352}{2465}-\left(\dfrac{26178347}{1440}-655\right)\\&=&-\dfrac{24551}{8262}+\dfrac{110352}{2465}-\dfrac{25235147}{1440}\\&=&\dfrac{50071177}{1197990}-\dfrac{25235147}{1440}\\&=&-\dfrac{30159351259650}{1725105600}\\ \end{eqnarray*}