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 \[\dfrac{\dfrac{9\times\left(\left(-7\right)\times\left(\dfrac{56}{9}+4-2\right)\times\left(-3\right)\times\left(-\dfrac{28}{3}\right)+\dfrac{84}{5}-9+\dfrac{28}{3}\right)\times\left(-6\right)}{2}}{\left(11+11\right)-\left(9-11-6-\dfrac{21}{11}+9+\dfrac{56}{9}+\left(-\dfrac{28}{3}\right)\times\left(-\dfrac{21}{4}\right)\times\left(-\dfrac{28}{3}\right)\times\dfrac{\dfrac{-\dfrac{44}{3}}{-\dfrac{28}{3}}}{-\dfrac{28}{3}}\times\left(-6\right)-\dfrac{21}{11}\right)+11}\]

Cliquer ici pour afficher la solution

Exercice

On a $ X=\dfrac{\dfrac{9\times\left(\left(-7\right)\times\left(\dfrac{56}{9}+4-2\right)\times\left(-3\right)\times\left(-\dfrac{28}{3}\right)+\dfrac{84}{5}-9+\dfrac{28}{3}\right)\times\left(-6\right)}{2}}{\left(11+11\right)-\left(9-11-6-\dfrac{21}{11}+9+\dfrac{56}{9}+\left(-\dfrac{28}{3}\right)\times\left(-\dfrac{21}{4}\right)\times\left(-\dfrac{28}{3}\right)\times\dfrac{\dfrac{-\dfrac{44}{3}}{-\dfrac{28}{3}}}{-\dfrac{28}{3}}\times\left(-6\right)-\dfrac{21}{11}\right)+11}=\dfrac{21309453}{243340}$ . Voici le détail : \begin{eqnarray*} X &=&\dfrac{\dfrac{9\times\left(\left(-7\right)\times\left(\dfrac{92}{9}-2\right)\times\left(-3\right)\times\left(-\dfrac{28}{3}\right)+\dfrac{84}{5}-9+\dfrac{28}{3}\right)\times\left(-6\right)}{2}}{\left(11+11\right)-\left(9-11-6-\dfrac{21}{11}+9+\dfrac{56}{9}+\left(-\dfrac{28}{3}\right)\times\left(-\dfrac{21}{4}\right)\times\left(-\dfrac{28}{3}\right)\times\dfrac{\dfrac{-\dfrac{44}{3}}{-\dfrac{28}{3}}}{-\dfrac{28}{3}}\times\left(-6\right)-\dfrac{21}{11}\right)+11}\\&=&\dfrac{\dfrac{9\times\left(\left(-7\right)\times\dfrac{74}{9}\times\left(-3\right)\times\left(-\dfrac{28}{3}\right)+\dfrac{84}{5}-9+\dfrac{28}{3}\right)\times\left(-6\right)}{2}}{\left(11+11\right)-\left(9-11-6-\dfrac{21}{11}+9+\dfrac{56}{9}+\left(-\dfrac{28}{3}\right)\times\left(-\dfrac{21}{4}\right)\times\left(-\dfrac{28}{3}\right)\times\dfrac{\dfrac{-\dfrac{44}{3}}{-\dfrac{28}{3}}}{-\dfrac{28}{3}}\times\left(-6\right)-\dfrac{21}{11}\right)+11}\\&=&\dfrac{\dfrac{9\times\left(\left(-7\right)\times\dfrac{74}{9}\times\left(-3\right)\times\left(-\dfrac{28}{3}\right)+\dfrac{84}{5}-9+\dfrac{28}{3}\right)\times\left(-6\right)}{2}}{\left(11+11\right)-\left(9-11-6+\dfrac{78}{11}+\dfrac{56}{9}+\left(-\dfrac{28}{3}\right)\times\left(-\dfrac{21}{4}\right)\times\left(-\dfrac{28}{3}\right)\times\dfrac{\dfrac{-\dfrac{44}{3}}{-\dfrac{28}{3}}}{-\dfrac{28}{3}}\times\left(-6\right)-\dfrac{21}{11}\right)+11}\\&=&\dfrac{\dfrac{9\times\left(\left(-7\right)\times\dfrac{74}{9}\times\left(-3\right)\times\left(-\dfrac{28}{3}\right)+\dfrac{84}{5}-9+\dfrac{28}{3}\right)\times\left(-6\right)}{2}}{\left(11+11\right)-\left(9-11-6+\dfrac{1318}{99}+\left(-\dfrac{28}{3}\right)\times\left(-\dfrac{21}{4}\right)\times\left(-\dfrac{28}{3}\right)\times\dfrac{\dfrac{-\dfrac{44}{3}}{-\dfrac{28}{3}}}{-\dfrac{28}{3}}\times\left(-6\right)-\dfrac{21}{11}\right)+11}\\&=&\dfrac{\dfrac{9\times\left(\left(-7\right)\times\dfrac{74}{9}\times\left(-3\right)\times\left(-\dfrac{28}{3}\right)+\dfrac{84}{5}-9+\dfrac{28}{3}\right)\times\left(-6\right)}{2}}{\left(11+11\right)-\left(9-11-6+\dfrac{1318}{99}+49\times\left(-\dfrac{28}{3}\right)\times\dfrac{\dfrac{-\dfrac{44}{3}}{-\dfrac{28}{3}}}{-\dfrac{28}{3}}\times\left(-6\right)-\dfrac{21}{11}\right)+11}\\&=&\dfrac{\dfrac{9\times\left(\left(-7\right)\times\dfrac{74}{9}\times\left(-3\right)\times\left(-\dfrac{28}{3}\right)+\dfrac{84}{5}-9+\dfrac{28}{3}\right)\times\left(-6\right)}{2}}{\left(11+11\right)-\left(9-11-6+\dfrac{1318}{99}+\left(-\dfrac{1372}{3}\right)\times\dfrac{\dfrac{-\dfrac{44}{3}}{-\dfrac{28}{3}}}{-\dfrac{28}{3}}\times\left(-6\right)-\dfrac{21}{11}\right)+11}\\&=&\dfrac{\dfrac{9\times\left(\left(-7\right)\times\dfrac{74}{9}\times\left(-3\right)\times\left(-\dfrac{28}{3}\right)+\dfrac{84}{5}-9+\dfrac{28}{3}\right)\times\left(-6\right)}{2}}{\left(11+11\right)-\left(9-11-6+\dfrac{1318}{99}+\left(-\dfrac{1372}{3}\right)\times\dfrac{\dfrac{11}{7}}{-\dfrac{28}{3}}\times\left(-6\right)-\dfrac{21}{11}\right)+11}\\&=&\dfrac{\dfrac{9\times\left(\left(-7\right)\times\dfrac{74}{9}\times\left(-3\right)\times\left(-\dfrac{28}{3}\right)+\dfrac{84}{5}-9+\dfrac{28}{3}\right)\times\left(-6\right)}{2}}{\left(11+11\right)-\left(9-11-6+\dfrac{1318}{99}+\left(-\dfrac{1372}{3}\right)\times\left(-\dfrac{33}{196}\right)\times\left(-6\right)-\dfrac{21}{11}\right)+11}\\&=&\dfrac{\dfrac{9\times\left(\left(-\dfrac{518}{9}\right)\times\left(-3\right)\times\left(-\dfrac{28}{3}\right)+\dfrac{84}{5}-9+\dfrac{28}{3}\right)\times\left(-6\right)}{2}}{\left(11+11\right)-\left(9-11-6+\dfrac{1318}{99}+\left(-\dfrac{1372}{3}\right)\times\left(-\dfrac{33}{196}\right)\times\left(-6\right)-\dfrac{21}{11}\right)+11}\\&=&\dfrac{\dfrac{9\times\left(\dfrac{518}{3}\times\left(-\dfrac{28}{3}\right)+\dfrac{84}{5}-9+\dfrac{28}{3}\right)\times\left(-6\right)}{2}}{\left(11+11\right)-\left(9-11-6+\dfrac{1318}{99}+\left(-\dfrac{1372}{3}\right)\times\left(-\dfrac{33}{196}\right)\times\left(-6\right)-\dfrac{21}{11}\right)+11}\\&=&\dfrac{\dfrac{9\times\left(-\dfrac{14504}{9}+\dfrac{84}{5}-9+\dfrac{28}{3}\right)\times\left(-6\right)}{2}}{\left(11+11\right)-\left(9-11-6+\dfrac{1318}{99}+\left(-\dfrac{1372}{3}\right)\times\left(-\dfrac{33}{196}\right)\times\left(-6\right)-\dfrac{21}{11}\right)+11}\\&=&\dfrac{\dfrac{9\times\left(-\dfrac{14504}{9}+\dfrac{84}{5}-9+\dfrac{28}{3}\right)\times\left(-6\right)}{2}}{\left(11+11\right)-\left(-2-6+\dfrac{1318}{99}+\left(-\dfrac{1372}{3}\right)\times\left(-\dfrac{33}{196}\right)\times\left(-6\right)-\dfrac{21}{11}\right)+11}\\&=&\dfrac{\dfrac{9\times\left(-\dfrac{14504}{9}+\dfrac{84}{5}-9+\dfrac{28}{3}\right)\times\left(-6\right)}{2}}{\left(11+11\right)-\left(-8+\dfrac{1318}{99}+\left(-\dfrac{1372}{3}\right)\times\left(-\dfrac{33}{196}\right)\times\left(-6\right)-\dfrac{21}{11}\right)+11}\\&=&\dfrac{\dfrac{9\times\left(-\dfrac{14504}{9}+\dfrac{84}{5}-9+\dfrac{28}{3}\right)\times\left(-6\right)}{2}}{\left(11+11\right)-\left(\dfrac{526}{99}+\left(-\dfrac{1372}{3}\right)\times\left(-\dfrac{33}{196}\right)\times\left(-6\right)-\dfrac{21}{11}\right)+11}\\&=&\dfrac{\dfrac{9\times\left(-\dfrac{14504}{9}+\dfrac{84}{5}-9+\dfrac{28}{3}\right)\times\left(-6\right)}{2}}{\left(11+11\right)-\left(\dfrac{526}{99}+77\times\left(-6\right)-\dfrac{21}{11}\right)+11}\\&=&\dfrac{\dfrac{9\times\left(-\dfrac{14504}{9}+\dfrac{84}{5}-9+\dfrac{28}{3}\right)\times\left(-6\right)}{2}}{\left(11+11\right)-\left(\dfrac{526}{99}-462-\dfrac{21}{11}\right)+11}\\&=&\dfrac{\dfrac{9\times\left(-\dfrac{71764}{45}-9+\dfrac{28}{3}\right)\times\left(-6\right)}{2}}{\left(11+11\right)-\left(\dfrac{526}{99}-462-\dfrac{21}{11}\right)+11}\\&=&\dfrac{\dfrac{9\times\left(-\dfrac{72169}{45}+\dfrac{28}{3}\right)\times\left(-6\right)}{2}}{\left(11+11\right)-\left(\dfrac{526}{99}-462-\dfrac{21}{11}\right)+11}\\&=&\dfrac{\dfrac{9\times\left(-\dfrac{71749}{45}\right)\times\left(-6\right)}{2}}{\left(11+11\right)-\left(\dfrac{526}{99}-462-\dfrac{21}{11}\right)+11}\\&=&\dfrac{\dfrac{9\times\left(-\dfrac{71749}{45}\right)\times\left(-6\right)}{2}}{22-\left(\dfrac{526}{99}-462-\dfrac{21}{11}\right)+11}\\&=&\dfrac{\dfrac{9\times\left(-\dfrac{71749}{45}\right)\times\left(-6\right)}{2}}{22-\left(-\dfrac{45212}{99}-\dfrac{21}{11}\right)+11}\\&=&\dfrac{\dfrac{9\times\left(-\dfrac{71749}{45}\right)\times\left(-6\right)}{2}}{22+\dfrac{45401}{99}+11}\\&=&\dfrac{\dfrac{\left(-\dfrac{71749}{5}\right)\times\left(-6\right)}{2}}{22+\dfrac{45401}{99}+11}\\&=&\dfrac{\dfrac{\dfrac{430494}{5}}{2}}{22+\dfrac{45401}{99}+11}\\&=&\dfrac{\dfrac{\dfrac{430494}{5}}{2}}{\dfrac{47579}{99}+11}\\&=&\dfrac{\dfrac{\dfrac{430494}{5}}{2}}{\dfrac{48668}{99}}\\&=&\dfrac{\dfrac{215247}{5}}{\dfrac{48668}{99}}\\&=&\dfrac{21309453}{243340}\\ \end{eqnarray*}