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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 \[\dfrac{\dfrac{\dfrac{\dfrac{41}{3}\times0\times\dfrac{91}{3}\times11}{\dfrac{117}{4}\times\left(-\dfrac{130}{7}-\left(\dfrac{\dfrac{\dfrac{53}{11}}{\dfrac{31}{7}}}{\dfrac{31}{7}}-\dfrac{67}{3}+3\right)\right)\times\dfrac{\dfrac{\dfrac{53}{11}}{3}}{-\dfrac{130}{7}}\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{\dfrac{\dfrac{91}{9}}{\dfrac{\dfrac{\dfrac{91}{3}}{0}}{11\times\dfrac{117}{4}\times\left(-\dfrac{67}{3}\right)}}+\left(\dfrac{\dfrac{\dfrac{\dfrac{31}{7}}{\dfrac{91}{3}}}{-7}}{0}-\dfrac{31}{3}-\dfrac{91}{3}+\dfrac{67}{3}\right)\times\dfrac{31}{7}}\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=\dfrac{\dfrac{\dfrac{\dfrac{41}{3}\times0\times\dfrac{91}{3}\times11}{\dfrac{117}{4}\times\left(-\dfrac{130}{7}-\left(\dfrac{\dfrac{\dfrac{53}{11}}{\dfrac{31}{7}}}{\dfrac{31}{7}}-\dfrac{67}{3}+3\right)\right)\times\dfrac{\dfrac{\dfrac{53}{11}}{3}}{-\dfrac{130}{7}}\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{\dfrac{\dfrac{91}{9}}{\dfrac{\dfrac{\dfrac{91}{3}}{0}}{11\times\dfrac{117}{4}\times\left(-\dfrac{67}{3}\right)}}+\left(\dfrac{\dfrac{\dfrac{\dfrac{31}{7}}{\dfrac{91}{3}}}{-7}}{0}-\dfrac{31}{3}-\dfrac{91}{3}+\dfrac{67}{3}\right)\times\dfrac{31}{7}}=0\) . Voici le détail : \begin{eqnarray*} X &=&\dfrac{\dfrac{\dfrac{\dfrac{41}{3}\times0\times\dfrac{91}{3}\times11}{\dfrac{117}{4}\times\left(-\dfrac{130}{7}-\left(\dfrac{\dfrac{371}{341}}{\dfrac{31}{7}}-\dfrac{67}{3}+3\right)\right)\times\dfrac{\dfrac{\dfrac{53}{11}}{3}}{-\dfrac{130}{7}}\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{\dfrac{\dfrac{91}{9}}{\dfrac{\dfrac{\dfrac{91}{3}}{0}}{11\times\dfrac{117}{4}\times\left(-\dfrac{67}{3}\right)}}+\left(\dfrac{\dfrac{\dfrac{\dfrac{31}{7}}{\dfrac{91}{3}}}{-7}}{0}-\dfrac{31}{3}-\dfrac{91}{3}+\dfrac{67}{3}\right)\times\dfrac{31}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{41}{3}\times0\times\dfrac{91}{3}\times11}{\dfrac{117}{4}\times\left(-\dfrac{130}{7}-\left(\dfrac{2597}{10571}-\dfrac{67}{3}+3\right)\right)\times\dfrac{\dfrac{\dfrac{53}{11}}{3}}{-\dfrac{130}{7}}\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{\dfrac{\dfrac{91}{9}}{\dfrac{\dfrac{\dfrac{91}{3}}{0}}{11\times\dfrac{117}{4}\times\left(-\dfrac{67}{3}\right)}}+\left(\dfrac{\dfrac{\dfrac{\dfrac{31}{7}}{\dfrac{91}{3}}}{-7}}{0}-\dfrac{31}{3}-\dfrac{91}{3}+\dfrac{67}{3}\right)\times\dfrac{31}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{41}{3}\times0\times\dfrac{91}{3}\times11}{\dfrac{117}{4}\times\left(-\dfrac{130}{7}-\left(\dfrac{2597}{10571}-\dfrac{67}{3}+3\right)\right)\times\dfrac{\dfrac{\dfrac{53}{11}}{3}}{-\dfrac{130}{7}}\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{\dfrac{\dfrac{91}{9}}{\dfrac{\dfrac{\dfrac{91}{3}}{0}}{\dfrac{1287}{4}\times\left(-\dfrac{67}{3}\right)}}+\left(\dfrac{\dfrac{\dfrac{\dfrac{31}{7}}{\dfrac{91}{3}}}{-7}}{0}-\dfrac{31}{3}-\dfrac{91}{3}+\dfrac{67}{3}\right)\times\dfrac{31}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{41}{3}\times0\times\dfrac{91}{3}\times11}{\dfrac{117}{4}\times\left(-\dfrac{130}{7}-\left(\dfrac{2597}{10571}-\dfrac{67}{3}+3\right)\right)\times\dfrac{\dfrac{\dfrac{53}{11}}{3}}{-\dfrac{130}{7}}\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{\dfrac{\dfrac{91}{9}}{\dfrac{\dfrac{\dfrac{91}{3}}{0}}{-\dfrac{28743}{4}}}+\left(\dfrac{\dfrac{\dfrac{\dfrac{31}{7}}{\dfrac{91}{3}}}{-7}}{0}-\dfrac{31}{3}-\dfrac{91}{3}+\dfrac{67}{3}\right)\times\dfrac{31}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{41}{3}\times0\times\dfrac{91}{3}\times11}{\dfrac{117}{4}\times\left(-\dfrac{130}{7}-\left(\dfrac{2597}{10571}-\dfrac{67}{3}+3\right)\right)\times\dfrac{\dfrac{\dfrac{53}{11}}{3}}{-\dfrac{130}{7}}\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{\dfrac{\dfrac{91}{9}}{\dfrac{\dfrac{\dfrac{91}{3}}{0}}{-\dfrac{28743}{4}}}+\left(\dfrac{\dfrac{\dfrac{93}{637}}{-7}}{0}-\dfrac{31}{3}-\dfrac{91}{3}+\dfrac{67}{3}\right)\times\dfrac{31}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{41}{3}\times0\times\dfrac{91}{3}\times11}{\dfrac{117}{4}\times\left(-\dfrac{130}{7}-\left(\dfrac{2597}{10571}-\dfrac{67}{3}+3\right)\right)\times\dfrac{\dfrac{\dfrac{53}{11}}{3}}{-\dfrac{130}{7}}\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{\dfrac{\dfrac{91}{9}}{\dfrac{\dfrac{\dfrac{91}{3}}{0}}{-\dfrac{28743}{4}}}+\left(\dfrac{-\dfrac{93}{4459}}{0}-\dfrac{31}{3}-\dfrac{91}{3}+\dfrac{67}{3}\right)\times\dfrac{31}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{41}{3}\times0\times\dfrac{91}{3}\times11}{\dfrac{117}{4}\times\left(-\dfrac{130}{7}-\left(\dfrac{2597}{10571}-\dfrac{67}{3}+3\right)\right)\times\dfrac{\dfrac{\dfrac{53}{11}}{3}}{-\dfrac{130}{7}}\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{\dfrac{\dfrac{91}{9}}{\dfrac{\dfrac{\dfrac{91}{3}}{0}}{-\dfrac{28743}{4}}}+\left(0-\dfrac{31}{3}-\dfrac{91}{3}+\dfrac{67}{3}\right)\times\dfrac{31}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{41}{3}\times0\times\dfrac{91}{3}\times11}{\dfrac{117}{4}\times\left(-\dfrac{130}{7}-\left(-\dfrac{700466}{31713}+3\right)\right)\times\dfrac{\dfrac{\dfrac{53}{11}}{3}}{-\dfrac{130}{7}}\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{\dfrac{\dfrac{91}{9}}{\dfrac{\dfrac{\dfrac{91}{3}}{0}}{-\dfrac{28743}{4}}}+\left(0-\dfrac{31}{3}-\dfrac{91}{3}+\dfrac{67}{3}\right)\times\dfrac{31}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{41}{3}\times0\times\dfrac{91}{3}\times11}{\dfrac{117}{4}\times\left(-\dfrac{130}{7}+\dfrac{605327}{31713}\right)\times\dfrac{\dfrac{\dfrac{53}{11}}{3}}{-\dfrac{130}{7}}\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{\dfrac{\dfrac{91}{9}}{\dfrac{\dfrac{\dfrac{91}{3}}{0}}{-\dfrac{28743}{4}}}+\left(0-\dfrac{31}{3}-\dfrac{91}{3}+\dfrac{67}{3}\right)\times\dfrac{31}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{41}{3}\times0\times\dfrac{91}{3}\times11}{\dfrac{117}{4}\times\left(-\dfrac{130}{7}+\dfrac{605327}{31713}\right)\times\dfrac{\dfrac{\dfrac{53}{11}}{3}}{-\dfrac{130}{7}}\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{\dfrac{\dfrac{91}{9}}{\dfrac{0}{-\dfrac{28743}{4}}}+\left(0-\dfrac{31}{3}-\dfrac{91}{3}+\dfrac{67}{3}\right)\times\dfrac{31}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{41}{3}\times0\times\dfrac{91}{3}\times11}{\dfrac{117}{4}\times\left(-\dfrac{130}{7}+\dfrac{605327}{31713}\right)\times\dfrac{\dfrac{\dfrac{53}{11}}{3}}{-\dfrac{130}{7}}\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{\dfrac{\dfrac{91}{9}}{0}+\left(0-\dfrac{31}{3}-\dfrac{91}{3}+\dfrac{67}{3}\right)\times\dfrac{31}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{41}{3}\times0\times\dfrac{91}{3}\times11}{\dfrac{117}{4}\times\left(-\dfrac{130}{7}+\dfrac{605327}{31713}\right)\times\dfrac{\dfrac{\dfrac{53}{11}}{3}}{-\dfrac{130}{7}}\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{\dfrac{\dfrac{91}{9}}{0}+\left(-\dfrac{31}{3}-\dfrac{91}{3}+\dfrac{67}{3}\right)\times\dfrac{31}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{41}{3}\times0\times\dfrac{91}{3}\times11}{\dfrac{117}{4}\times\left(-\dfrac{130}{7}+\dfrac{605327}{31713}\right)\times\dfrac{\dfrac{\dfrac{53}{11}}{3}}{-\dfrac{130}{7}}\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{\dfrac{\dfrac{91}{9}}{0}+\left(-\dfrac{122}{3}+\dfrac{67}{3}\right)\times\dfrac{31}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{41}{3}\times0\times\dfrac{91}{3}\times11}{\dfrac{117}{4}\times\left(-\dfrac{130}{7}+\dfrac{605327}{31713}\right)\times\dfrac{\dfrac{\dfrac{53}{11}}{3}}{-\dfrac{130}{7}}\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{\dfrac{\dfrac{91}{9}}{0}+\left(-\dfrac{55}{3}\right)\times\dfrac{31}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{41}{3}\times0\times\dfrac{91}{3}\times11}{\dfrac{117}{4}\times\dfrac{114599}{221991}\times\dfrac{\dfrac{\dfrac{53}{11}}{3}}{-\dfrac{130}{7}}\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{\dfrac{\dfrac{91}{9}}{0}+\left(-\dfrac{55}{3}\right)\times\dfrac{31}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{41}{3}\times0\times\dfrac{91}{3}\times11}{\dfrac{117}{4}\times\dfrac{114599}{221991}\times\dfrac{\dfrac{53}{33}}{-\dfrac{130}{7}}\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{\dfrac{\dfrac{91}{9}}{0}+\left(-\dfrac{55}{3}\right)\times\dfrac{31}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{41}{3}\times0\times\dfrac{91}{3}\times11}{\dfrac{117}{4}\times\dfrac{114599}{221991}\times\left(-\dfrac{371}{4290}\right)\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{\dfrac{\dfrac{91}{9}}{0}+\left(-\dfrac{55}{3}\right)\times\dfrac{31}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{41}{3}\times0\times\dfrac{91}{3}\times11}{\dfrac{117}{4}\times\dfrac{114599}{221991}\times\left(-\dfrac{371}{4290}\right)\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{0+\left(-\dfrac{55}{3}\right)\times\dfrac{31}{7}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{41}{3}\times0\times\dfrac{91}{3}\times11}{\dfrac{117}{4}\times\dfrac{114599}{221991}\times\left(-\dfrac{371}{4290}\right)\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{0-\dfrac{1705}{21}}\\&=&\dfrac{\dfrac{\dfrac{0\times\dfrac{91}{3}\times11}{\dfrac{117}{4}\times\dfrac{114599}{221991}\times\left(-\dfrac{371}{4290}\right)\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{0-\dfrac{1705}{21}}\\&=&\dfrac{\dfrac{\dfrac{0\times11}{\dfrac{117}{4}\times\dfrac{114599}{221991}\times\left(-\dfrac{371}{4290}\right)\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{0-\dfrac{1705}{21}}\\&=&\dfrac{\dfrac{\dfrac{0}{\dfrac{117}{4}\times\dfrac{114599}{221991}\times\left(-\dfrac{371}{4290}\right)\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{0-\dfrac{1705}{21}}\\&=&\dfrac{\dfrac{\dfrac{0}{\dfrac{4469361}{295988}\times\left(-\dfrac{371}{4290}\right)\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{0-\dfrac{1705}{21}}\\&=&\dfrac{\dfrac{\dfrac{0}{\left(-\dfrac{6073747}{4651240}\right)\times\dfrac{53}{11}}}{\dfrac{117}{4}}}{0-\dfrac{1705}{21}}\\&=&\dfrac{\dfrac{\dfrac{0}{-\dfrac{321908591}{51163640}}}{\dfrac{117}{4}}}{0-\dfrac{1705}{21}}\\&=&\dfrac{\dfrac{\dfrac{0}{-\dfrac{321908591}{51163640}}}{\dfrac{117}{4}}}{-\dfrac{1705}{21}}\\&=&\dfrac{\dfrac{0}{\dfrac{117}{4}}}{-\dfrac{1705}{21}}\\&=&\dfrac{0}{-\dfrac{1705}{21}}\\&=&0\\ \end{eqnarray*}