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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 \[\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-2}{\dfrac{\dfrac{-\dfrac{141}{11}}{6+\dfrac{103}{10}}}{-\dfrac{141}{11}}}}{\dfrac{97}{3}}}{-\dfrac{141}{11}-6+\dfrac{141}{11}+\dfrac{\dfrac{-10}{-10}}{6}-\dfrac{118}{7}-\dfrac{141}{11}}}{\dfrac{103}{10}\times\dfrac{1}{-10}\times\dfrac{\dfrac{1}{\dfrac{\dfrac{-\dfrac{118}{7}}{1}}{4}+10}}{\dfrac{31}{2}}}}{\dfrac{97}{3}}\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-2}{\dfrac{\dfrac{-\dfrac{141}{11}}{6+\dfrac{103}{10}}}{-\dfrac{141}{11}}}}{\dfrac{97}{3}}}{-\dfrac{141}{11}-6+\dfrac{141}{11}+\dfrac{\dfrac{-10}{-10}}{6}-\dfrac{118}{7}-\dfrac{141}{11}}}{\dfrac{103}{10}\times\dfrac{1}{-10}\times\dfrac{\dfrac{1}{\dfrac{\dfrac{-\dfrac{118}{7}}{1}}{4}+10}}{\dfrac{31}{2}}}}{\dfrac{97}{3}}=-\dfrac{42546007350}{556448495225}\) . Voici le détail : \begin{eqnarray*} X &=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-2}{\dfrac{\dfrac{-\dfrac{141}{11}}{\dfrac{163}{10}}}{-\dfrac{141}{11}}}}{\dfrac{97}{3}}}{-\dfrac{141}{11}-6+\dfrac{141}{11}+\dfrac{\dfrac{-10}{-10}}{6}-\dfrac{118}{7}-\dfrac{141}{11}}}{\dfrac{103}{10}\times\dfrac{1}{-10}\times\dfrac{\dfrac{1}{\dfrac{\dfrac{-\dfrac{118}{7}}{1}}{4}+10}}{\dfrac{31}{2}}}}{\dfrac{97}{3}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-2}{\dfrac{\dfrac{-\dfrac{141}{11}}{\dfrac{163}{10}}}{-\dfrac{141}{11}}}}{\dfrac{97}{3}}}{-\dfrac{207}{11}+\dfrac{141}{11}+\dfrac{\dfrac{-10}{-10}}{6}-\dfrac{118}{7}-\dfrac{141}{11}}}{\dfrac{103}{10}\times\dfrac{1}{-10}\times\dfrac{\dfrac{1}{\dfrac{\dfrac{-\dfrac{118}{7}}{1}}{4}+10}}{\dfrac{31}{2}}}}{\dfrac{97}{3}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-2}{\dfrac{\dfrac{-\dfrac{141}{11}}{\dfrac{163}{10}}}{-\dfrac{141}{11}}}}{\dfrac{97}{3}}}{-6+\dfrac{\dfrac{-10}{-10}}{6}-\dfrac{118}{7}-\dfrac{141}{11}}}{\dfrac{103}{10}\times\dfrac{1}{-10}\times\dfrac{\dfrac{1}{\dfrac{\dfrac{-\dfrac{118}{7}}{1}}{4}+10}}{\dfrac{31}{2}}}}{\dfrac{97}{3}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-2}{\dfrac{\dfrac{-\dfrac{141}{11}}{\dfrac{163}{10}}}{-\dfrac{141}{11}}}}{\dfrac{97}{3}}}{-6+\dfrac{1}{6}-\dfrac{118}{7}-\dfrac{141}{11}}}{\dfrac{103}{10}\times\dfrac{1}{-10}\times\dfrac{\dfrac{1}{\dfrac{\dfrac{-\dfrac{118}{7}}{1}}{4}+10}}{\dfrac{31}{2}}}}{\dfrac{97}{3}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-2}{\dfrac{\dfrac{-\dfrac{141}{11}}{\dfrac{163}{10}}}{-\dfrac{141}{11}}}}{\dfrac{97}{3}}}{-6+\dfrac{1}{6}-\dfrac{118}{7}-\dfrac{141}{11}}}{\dfrac{103}{10}\times\dfrac{1}{-10}\times\dfrac{\dfrac{1}{\dfrac{\dfrac{-\dfrac{118}{7}}{1}}{4}+10}}{\dfrac{31}{2}}}}{\dfrac{97}{3}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-2}{\dfrac{\dfrac{-\dfrac{141}{11}}{\dfrac{163}{10}}}{-\dfrac{141}{11}}}}{\dfrac{97}{3}}}{-6+\dfrac{1}{6}-\dfrac{118}{7}-\dfrac{141}{11}}}{\dfrac{103}{10}\times\dfrac{1}{-10}\times\dfrac{\dfrac{1}{\dfrac{-\dfrac{118}{7}}{4}+10}}{\dfrac{31}{2}}}}{\dfrac{97}{3}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-2}{\dfrac{\dfrac{-\dfrac{141}{11}}{\dfrac{163}{10}}}{-\dfrac{141}{11}}}}{\dfrac{97}{3}}}{-6+\dfrac{1}{6}-\dfrac{118}{7}-\dfrac{141}{11}}}{\dfrac{103}{10}\times\dfrac{1}{-10}\times\dfrac{\dfrac{1}{-\dfrac{59}{14}+10}}{\dfrac{31}{2}}}}{\dfrac{97}{3}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-2}{\dfrac{-\dfrac{1410}{1793}}{-\dfrac{141}{11}}}}{\dfrac{97}{3}}}{-6+\dfrac{1}{6}-\dfrac{118}{7}-\dfrac{141}{11}}}{\dfrac{103}{10}\times\dfrac{1}{-10}\times\dfrac{\dfrac{1}{-\dfrac{59}{14}+10}}{\dfrac{31}{2}}}}{\dfrac{97}{3}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-2}{\dfrac{10}{163}}}{\dfrac{97}{3}}}{-6+\dfrac{1}{6}-\dfrac{118}{7}-\dfrac{141}{11}}}{\dfrac{103}{10}\times\dfrac{1}{-10}\times\dfrac{\dfrac{1}{-\dfrac{59}{14}+10}}{\dfrac{31}{2}}}}{\dfrac{97}{3}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-2}{\dfrac{10}{163}}}{\dfrac{97}{3}}}{-\dfrac{35}{6}-\dfrac{118}{7}-\dfrac{141}{11}}}{\dfrac{103}{10}\times\dfrac{1}{-10}\times\dfrac{\dfrac{1}{-\dfrac{59}{14}+10}}{\dfrac{31}{2}}}}{\dfrac{97}{3}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-2}{\dfrac{10}{163}}}{\dfrac{97}{3}}}{-\dfrac{35}{6}-\dfrac{2285}{77}}}{\dfrac{103}{10}\times\dfrac{1}{-10}\times\dfrac{\dfrac{1}{-\dfrac{59}{14}+10}}{\dfrac{31}{2}}}}{\dfrac{97}{3}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-2}{\dfrac{10}{163}}}{\dfrac{97}{3}}}{-\dfrac{35}{6}-\dfrac{2285}{77}}}{\dfrac{103}{10}\times\dfrac{1}{-10}\times\dfrac{\dfrac{1}{\dfrac{81}{14}}}{\dfrac{31}{2}}}}{\dfrac{97}{3}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{163}{5}}{\dfrac{97}{3}}}{-\dfrac{35}{6}-\dfrac{2285}{77}}}{\dfrac{103}{10}\times\dfrac{1}{-10}\times\dfrac{\dfrac{1}{\dfrac{81}{14}}}{\dfrac{31}{2}}}}{\dfrac{97}{3}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{489}{485}}{-\dfrac{35}{6}-\dfrac{2285}{77}}}{\dfrac{103}{10}\times\dfrac{1}{-10}\times\dfrac{\dfrac{1}{\dfrac{81}{14}}}{\dfrac{31}{2}}}}{\dfrac{97}{3}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{489}{485}}{-\dfrac{16405}{462}}}{\dfrac{103}{10}\times\dfrac{1}{-10}\times\dfrac{\dfrac{1}{\dfrac{81}{14}}}{\dfrac{31}{2}}}}{\dfrac{97}{3}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{489}{485}}{-\dfrac{16405}{462}}}{\dfrac{103}{10}\times\left(-\dfrac{1}{10}\right)\times\dfrac{\dfrac{1}{\dfrac{81}{14}}}{\dfrac{31}{2}}}}{\dfrac{97}{3}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{489}{485}}{-\dfrac{16405}{462}}}{\dfrac{103}{10}\times\left(-\dfrac{1}{10}\right)\times\dfrac{\dfrac{14}{81}}{\dfrac{31}{2}}}}{\dfrac{97}{3}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{489}{485}}{-\dfrac{16405}{462}}}{\dfrac{103}{10}\times\left(-\dfrac{1}{10}\right)\times\dfrac{28}{2511}}}{\dfrac{97}{3}}\\&=&\dfrac{\dfrac{\dfrac{225918}{7956425}}{\dfrac{103}{10}\times\left(-\dfrac{1}{10}\right)\times\dfrac{28}{2511}}}{\dfrac{97}{3}}\\&=&\dfrac{\dfrac{\dfrac{225918}{7956425}}{\left(-\dfrac{103}{100}\right)\times\dfrac{28}{2511}}}{\dfrac{97}{3}}\\&=&\dfrac{\dfrac{\dfrac{225918}{7956425}}{-\dfrac{721}{62775}}}{\dfrac{97}{3}}\\&=&\dfrac{-\dfrac{14182002450}{5736582425}}{\dfrac{97}{3}}\\&=&-\dfrac{42546007350}{556448495225}\\ \end{eqnarray*}