L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\dfrac{\dfrac{\left(-\dfrac{49}{8}+5+\left(-7\right)\times\dfrac{122}{3}\times\left(-7\right)\right)\times\dfrac{59}{3}\times\left(-7\right)\times\left(\dfrac{5}{12}\times\left(-11\right)-\left(\dfrac{63}{2}+6+2\right)-\dfrac{63}{2}\right)\times\left(-7\right)}{-7+\dfrac{59}{3}+\dfrac{72}{5}+5}}{-11}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{\dfrac{\left(-\dfrac{49}{8}+5+\left(-7\right)\times\dfrac{122}{3}\times\left(-7\right)\right)\times\dfrac{59}{3}\times\left(-7\right)\times\left(\dfrac{5}{12}\times\left(-11\right)-\left(\dfrac{63}{2}+6+2\right)-\dfrac{63}{2}\right)\times\left(-7\right)}{-7+\dfrac{59}{3}+\dfrac{72}{5}+5}}{-11}=\dfrac{1879954232835}{4571424}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{\left(-\dfrac{49}{8}+5+\left(-7\right)\times\dfrac{122}{3}\times\left(-7\right)\right)\times\dfrac{59}{3}\times\left(-7\right)\times\left(-\dfrac{55}{12}-\left(\dfrac{63}{2}+6+2\right)-\dfrac{63}{2}\right)\times\left(-7\right)}{-7+\dfrac{59}{3}+\dfrac{72}{5}+5}}{-11}\\&=&\dfrac{\dfrac{\left(-\dfrac{49}{8}+5+\left(-7\right)\times\dfrac{122}{3}\times\left(-7\right)\right)\times\dfrac{59}{3}\times\left(-7\right)\times\left(-\dfrac{55}{12}-\left(\dfrac{75}{2}+2\right)-\dfrac{63}{2}\right)\times\left(-7\right)}{-7+\dfrac{59}{3}+\dfrac{72}{5}+5}}{-11}\\&=&\dfrac{\dfrac{\left(-\dfrac{49}{8}+5+\left(-7\right)\times\dfrac{122}{3}\times\left(-7\right)\right)\times\dfrac{59}{3}\times\left(-7\right)\times\left(-\dfrac{55}{12}-\dfrac{79}{2}-\dfrac{63}{2}\right)\times\left(-7\right)}{-7+\dfrac{59}{3}+\dfrac{72}{5}+5}}{-11}\\&=&\dfrac{\dfrac{\left(-\dfrac{49}{8}+5+\left(-\dfrac{854}{3}\right)\times\left(-7\right)\right)\times\dfrac{59}{3}\times\left(-7\right)\times\left(-\dfrac{55}{12}-\dfrac{79}{2}-\dfrac{63}{2}\right)\times\left(-7\right)}{-7+\dfrac{59}{3}+\dfrac{72}{5}+5}}{-11}\\&=&\dfrac{\dfrac{\left(-\dfrac{49}{8}+5+\dfrac{5978}{3}\right)\times\dfrac{59}{3}\times\left(-7\right)\times\left(-\dfrac{55}{12}-\dfrac{79}{2}-\dfrac{63}{2}\right)\times\left(-7\right)}{-7+\dfrac{59}{3}+\dfrac{72}{5}+5}}{-11}\\&=&\dfrac{\dfrac{\left(-\dfrac{49}{8}+5+\dfrac{5978}{3}\right)\times\dfrac{59}{3}\times\left(-7\right)\times\left(-\dfrac{529}{12}-\dfrac{63}{2}\right)\times\left(-7\right)}{-7+\dfrac{59}{3}+\dfrac{72}{5}+5}}{-11}\\&=&\dfrac{\dfrac{\left(-\dfrac{49}{8}+5+\dfrac{5978}{3}\right)\times\dfrac{59}{3}\times\left(-7\right)\times\left(-\dfrac{907}{12}\right)\times\left(-7\right)}{-7+\dfrac{59}{3}+\dfrac{72}{5}+5}}{-11}\\&=&\dfrac{\dfrac{\left(-\dfrac{9}{8}+\dfrac{5978}{3}\right)\times\dfrac{59}{3}\times\left(-7\right)\times\left(-\dfrac{907}{12}\right)\times\left(-7\right)}{-7+\dfrac{59}{3}+\dfrac{72}{5}+5}}{-11}\\&=&\dfrac{\dfrac{\dfrac{47797}{24}\times\dfrac{59}{3}\times\left(-7\right)\times\left(-\dfrac{907}{12}\right)\times\left(-7\right)}{-7+\dfrac{59}{3}+\dfrac{72}{5}+5}}{-11}\\&=&\dfrac{\dfrac{\dfrac{47797}{24}\times\dfrac{59}{3}\times\dfrac{6349}{12}\times\left(-7\right)}{-7+\dfrac{59}{3}+\dfrac{72}{5}+5}}{-11}\\&=&\dfrac{\dfrac{\dfrac{2820023}{72}\times\dfrac{6349}{12}\times\left(-7\right)}{-7+\dfrac{59}{3}+\dfrac{72}{5}+5}}{-11}\\&=&\dfrac{\dfrac{\dfrac{17904326027}{864}\times\left(-7\right)}{-7+\dfrac{59}{3}+\dfrac{72}{5}+5}}{-11}\\&=&\dfrac{\dfrac{-\dfrac{125330282189}{864}}{-7+\dfrac{59}{3}+\dfrac{72}{5}+5}}{-11}\\&=&\dfrac{\dfrac{-\dfrac{125330282189}{864}}{\dfrac{38}{3}+\dfrac{72}{5}+5}}{-11}\\&=&\dfrac{\dfrac{-\dfrac{125330282189}{864}}{\dfrac{406}{15}+5}}{-11}\\&=&\dfrac{\dfrac{-\dfrac{125330282189}{864}}{\dfrac{481}{15}}}{-11}\\&=&\dfrac{-\dfrac{1879954232835}{415584}}{-11}\\&=&\dfrac{1879954232835}{4571424}\\
\end{eqnarray*}