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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 \[\dfrac{\dfrac{\dfrac{\dfrac{6}{-7}}{\dfrac{133}{2}}}{\dfrac{\dfrac{-7}{\dfrac{\dfrac{\left(-3\right)\times\dfrac{11}{3}\times\dfrac{65}{4}}{-3}}{\dfrac{79}{7}+\dfrac{79}{7}-8}}}{\dfrac{43}{9}}}}{9\times4}-\left(\left(\dfrac{43}{9}+9+\dfrac{133}{2}\times\left(-\dfrac{83}{11}\right)\times\left(-3\right)\right)-\dfrac{7}{2}-\dfrac{7}{2}+\dfrac{\dfrac{\dfrac{43}{9}}{4}}{-\dfrac{142}{7}}-\dfrac{142}{7}\right)\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=\dfrac{\dfrac{\dfrac{\dfrac{6}{-7}}{\dfrac{133}{2}}}{\dfrac{\dfrac{-7}{\dfrac{\dfrac{\left(-3\right)\times\dfrac{11}{3}\times\dfrac{65}{4}}{-3}}{\dfrac{79}{7}+\dfrac{79}{7}-8}}}{\dfrac{43}{9}}}}{9\times4}-\left(\left(\dfrac{43}{9}+9+\dfrac{133}{2}\times\left(-\dfrac{83}{11}\right)\times\left(-3\right)\right)-\dfrac{7}{2}-\dfrac{7}{2}+\dfrac{\dfrac{\dfrac{43}{9}}{4}}{-\dfrac{142}{7}}-\dfrac{142}{7}\right)=-\dfrac{6022146707923584}{4036966807104}\) . Voici le détail : \begin{eqnarray*} X &=&\dfrac{\dfrac{\dfrac{\dfrac{6}{-7}}{\dfrac{133}{2}}}{\dfrac{\dfrac{-7}{\dfrac{\dfrac{\left(-11\right)\times\dfrac{65}{4}}{-3}}{\dfrac{79}{7}+\dfrac{79}{7}-8}}}{\dfrac{43}{9}}}}{9\times4}-\left(\left(\dfrac{43}{9}+9+\dfrac{133}{2}\times\left(-\dfrac{83}{11}\right)\times\left(-3\right)\right)-\dfrac{7}{2}-\dfrac{7}{2}+\dfrac{\dfrac{\dfrac{43}{9}}{4}}{-\dfrac{142}{7}}-\dfrac{142}{7}\right)\\&=&\dfrac{\dfrac{\dfrac{\dfrac{6}{-7}}{\dfrac{133}{2}}}{\dfrac{\dfrac{-7}{\dfrac{\dfrac{-\dfrac{715}{4}}{-3}}{\dfrac{79}{7}+\dfrac{79}{7}-8}}}{\dfrac{43}{9}}}}{9\times4}-\left(\left(\dfrac{43}{9}+9+\dfrac{133}{2}\times\left(-\dfrac{83}{11}\right)\times\left(-3\right)\right)-\dfrac{7}{2}-\dfrac{7}{2}+\dfrac{\dfrac{\dfrac{43}{9}}{4}}{-\dfrac{142}{7}}-\dfrac{142}{7}\right)\\&=&\dfrac{\dfrac{\dfrac{\dfrac{6}{-7}}{\dfrac{133}{2}}}{\dfrac{\dfrac{-7}{\dfrac{\dfrac{-\dfrac{715}{4}}{-3}}{\dfrac{158}{7}-8}}}{\dfrac{43}{9}}}}{9\times4}-\left(\left(\dfrac{43}{9}+9+\dfrac{133}{2}\times\left(-\dfrac{83}{11}\right)\times\left(-3\right)\right)-\dfrac{7}{2}-\dfrac{7}{2}+\dfrac{\dfrac{\dfrac{43}{9}}{4}}{-\dfrac{142}{7}}-\dfrac{142}{7}\right)\\&=&\dfrac{\dfrac{\dfrac{\dfrac{6}{-7}}{\dfrac{133}{2}}}{\dfrac{\dfrac{-7}{\dfrac{\dfrac{-\dfrac{715}{4}}{-3}}{\dfrac{102}{7}}}}{\dfrac{43}{9}}}}{9\times4}-\left(\left(\dfrac{43}{9}+9+\dfrac{133}{2}\times\left(-\dfrac{83}{11}\right)\times\left(-3\right)\right)-\dfrac{7}{2}-\dfrac{7}{2}+\dfrac{\dfrac{\dfrac{43}{9}}{4}}{-\dfrac{142}{7}}-\dfrac{142}{7}\right)\\&=&\dfrac{\dfrac{\dfrac{\dfrac{6}{-7}}{\dfrac{133}{2}}}{\dfrac{\dfrac{-7}{\dfrac{\dfrac{-\dfrac{715}{4}}{-3}}{\dfrac{102}{7}}}}{\dfrac{43}{9}}}}{9\times4}-\left(\left(\dfrac{43}{9}+9+\left(-\dfrac{11039}{22}\right)\times\left(-3\right)\right)-\dfrac{7}{2}-\dfrac{7}{2}+\dfrac{\dfrac{\dfrac{43}{9}}{4}}{-\dfrac{142}{7}}-\dfrac{142}{7}\right)\\&=&\dfrac{\dfrac{\dfrac{\dfrac{6}{-7}}{\dfrac{133}{2}}}{\dfrac{\dfrac{-7}{\dfrac{\dfrac{-\dfrac{715}{4}}{-3}}{\dfrac{102}{7}}}}{\dfrac{43}{9}}}}{9\times4}-\left(\left(\dfrac{43}{9}+9+\dfrac{33117}{22}\right)-\dfrac{7}{2}-\dfrac{7}{2}+\dfrac{\dfrac{\dfrac{43}{9}}{4}}{-\dfrac{142}{7}}-\dfrac{142}{7}\right)\\&=&\dfrac{\dfrac{\dfrac{\dfrac{6}{-7}}{\dfrac{133}{2}}}{\dfrac{\dfrac{-7}{\dfrac{\dfrac{715}{12}}{\dfrac{102}{7}}}}{\dfrac{43}{9}}}}{9\times4}-\left(\left(\dfrac{43}{9}+9+\dfrac{33117}{22}\right)-\dfrac{7}{2}-\dfrac{7}{2}+\dfrac{\dfrac{\dfrac{43}{9}}{4}}{-\dfrac{142}{7}}-\dfrac{142}{7}\right)\\&=&\dfrac{\dfrac{\dfrac{\dfrac{6}{-7}}{\dfrac{133}{2}}}{\dfrac{\dfrac{-7}{\dfrac{5005}{1224}}}{\dfrac{43}{9}}}}{9\times4}-\left(\left(\dfrac{43}{9}+9+\dfrac{33117}{22}\right)-\dfrac{7}{2}-\dfrac{7}{2}+\dfrac{\dfrac{\dfrac{43}{9}}{4}}{-\dfrac{142}{7}}-\dfrac{142}{7}\right)\\&=&\dfrac{\dfrac{\dfrac{\dfrac{6}{-7}}{\dfrac{133}{2}}}{\dfrac{\dfrac{-7}{\dfrac{5005}{1224}}}{\dfrac{43}{9}}}}{9\times4}-\left(\left(\dfrac{124}{9}+\dfrac{33117}{22}\right)-\dfrac{7}{2}-\dfrac{7}{2}+\dfrac{\dfrac{\dfrac{43}{9}}{4}}{-\dfrac{142}{7}}-\dfrac{142}{7}\right)\\&=&\dfrac{\dfrac{\dfrac{\dfrac{6}{-7}}{\dfrac{133}{2}}}{\dfrac{\dfrac{-7}{\dfrac{5005}{1224}}}{\dfrac{43}{9}}}}{9\times4}-\left(\dfrac{300781}{198}-\dfrac{7}{2}-\dfrac{7}{2}+\dfrac{\dfrac{\dfrac{43}{9}}{4}}{-\dfrac{142}{7}}-\dfrac{142}{7}\right)\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{6}{7}}{\dfrac{133}{2}}}{\dfrac{\dfrac{-7}{\dfrac{5005}{1224}}}{\dfrac{43}{9}}}}{9\times4}-\left(\dfrac{300781}{198}-\dfrac{7}{2}-\dfrac{7}{2}+\dfrac{\dfrac{\dfrac{43}{9}}{4}}{-\dfrac{142}{7}}-\dfrac{142}{7}\right)\\&=&\dfrac{\dfrac{-\dfrac{12}{931}}{\dfrac{\dfrac{-7}{\dfrac{5005}{1224}}}{\dfrac{43}{9}}}}{9\times4}-\left(\dfrac{300781}{198}-\dfrac{7}{2}-\dfrac{7}{2}+\dfrac{\dfrac{\dfrac{43}{9}}{4}}{-\dfrac{142}{7}}-\dfrac{142}{7}\right)\\&=&\dfrac{\dfrac{-\dfrac{12}{931}}{\dfrac{-\dfrac{1224}{715}}{\dfrac{43}{9}}}}{9\times4}-\left(\dfrac{300781}{198}-\dfrac{7}{2}-\dfrac{7}{2}+\dfrac{\dfrac{\dfrac{43}{9}}{4}}{-\dfrac{142}{7}}-\dfrac{142}{7}\right)\\&=&\dfrac{\dfrac{-\dfrac{12}{931}}{-\dfrac{11016}{30745}}}{9\times4}-\left(\dfrac{300781}{198}-\dfrac{7}{2}-\dfrac{7}{2}+\dfrac{\dfrac{\dfrac{43}{9}}{4}}{-\dfrac{142}{7}}-\dfrac{142}{7}\right)\\&=&\dfrac{\dfrac{-\dfrac{12}{931}}{-\dfrac{11016}{30745}}}{36}-\left(\dfrac{300781}{198}-\dfrac{7}{2}-\dfrac{7}{2}+\dfrac{\dfrac{\dfrac{43}{9}}{4}}{-\dfrac{142}{7}}-\dfrac{142}{7}\right)\\&=&\dfrac{\dfrac{-\dfrac{12}{931}}{-\dfrac{11016}{30745}}}{36}-\left(\dfrac{150044}{99}-\dfrac{7}{2}+\dfrac{\dfrac{\dfrac{43}{9}}{4}}{-\dfrac{142}{7}}-\dfrac{142}{7}\right)\\&=&\dfrac{\dfrac{-\dfrac{12}{931}}{-\dfrac{11016}{30745}}}{36}-\left(\dfrac{299395}{198}+\dfrac{\dfrac{\dfrac{43}{9}}{4}}{-\dfrac{142}{7}}-\dfrac{142}{7}\right)\\&=&\dfrac{\dfrac{-\dfrac{12}{931}}{-\dfrac{11016}{30745}}}{36}-\left(\dfrac{299395}{198}+\dfrac{\dfrac{43}{36}}{-\dfrac{142}{7}}-\dfrac{142}{7}\right)\\&=&\dfrac{\dfrac{-\dfrac{12}{931}}{-\dfrac{11016}{30745}}}{36}-\left(\dfrac{299395}{198}-\dfrac{301}{5112}-\dfrac{142}{7}\right)\\&=&\dfrac{\dfrac{30745}{854658}}{36}-\left(\dfrac{299395}{198}-\dfrac{301}{5112}-\dfrac{142}{7}\right)\\&=&\dfrac{30745}{30767688}-\left(\dfrac{299395}{198}-\dfrac{301}{5112}-\dfrac{142}{7}\right)\\&=&\dfrac{30745}{30767688}-\left(\dfrac{28341623}{18744}-\dfrac{142}{7}\right)\\&=&\dfrac{30745}{30767688}-\dfrac{195729713}{131208}\\&=&-\dfrac{6022146707923584}{4036966807104}\\ \end{eqnarray*}