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 \[\left(\dfrac{\left(-9\right)\times\dfrac{5}{3}}{2-\dfrac{-\dfrac{52}{11}}{\dfrac{5}{3}}+9}-\left(\dfrac{18}{5}-2-12\right)+12\right)-\left(-\dfrac{45}{4}+\dfrac{77}{8}\right)-\dfrac{18}{5}\times\left(-3\right)\times7\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\left(\dfrac{\left(-9\right)\times\dfrac{5}{3}}{2-\dfrac{-\dfrac{52}{11}}{\dfrac{5}{3}}+9}-\left(\dfrac{18}{5}-2-12\right)+12\right)-\left(-\dfrac{45}{4}+\dfrac{77}{8}\right)-\dfrac{18}{5}\times\left(-3\right)\times7=\dfrac{599917}{6088}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(\dfrac{\left(-9\right)\times\dfrac{5}{3}}{2+\dfrac{156}{55}+9}-\left(\dfrac{18}{5}-2-12\right)+12\right)-\left(-\dfrac{45}{4}+\dfrac{77}{8}\right)-\dfrac{18}{5}\times\left(-3\right)\times7\\&=&\left(\dfrac{-15}{2+\dfrac{156}{55}+9}-\left(\dfrac{18}{5}-2-12\right)+12\right)-\left(-\dfrac{45}{4}+\dfrac{77}{8}\right)-\dfrac{18}{5}\times\left(-3\right)\times7\\&=&\left(\dfrac{-15}{\dfrac{266}{55}+9}-\left(\dfrac{18}{5}-2-12\right)+12\right)-\left(-\dfrac{45}{4}+\dfrac{77}{8}\right)-\dfrac{18}{5}\times\left(-3\right)\times7\\&=&\left(\dfrac{-15}{\dfrac{761}{55}}-\left(\dfrac{18}{5}-2-12\right)+12\right)-\left(-\dfrac{45}{4}+\dfrac{77}{8}\right)-\dfrac{18}{5}\times\left(-3\right)\times7\\&=&\left(-\dfrac{825}{761}-\left(\dfrac{18}{5}-2-12\right)+12\right)-\left(-\dfrac{45}{4}+\dfrac{77}{8}\right)-\dfrac{18}{5}\times\left(-3\right)\times7\\&=&\left(-\dfrac{825}{761}-\left(\dfrac{8}{5}-12\right)+12\right)-\left(-\dfrac{45}{4}+\dfrac{77}{8}\right)-\dfrac{18}{5}\times\left(-3\right)\times7\\&=&\left(-\dfrac{825}{761}+\dfrac{52}{5}+12\right)-\left(-\dfrac{45}{4}+\dfrac{77}{8}\right)-\dfrac{18}{5}\times\left(-3\right)\times7\\&=&\left(\dfrac{35447}{3805}+12\right)-\left(-\dfrac{45}{4}+\dfrac{77}{8}\right)-\dfrac{18}{5}\times\left(-3\right)\times7\\&=&\dfrac{81107}{3805}-\left(-\dfrac{45}{4}+\dfrac{77}{8}\right)-\dfrac{18}{5}\times\left(-3\right)\times7\\&=&\dfrac{81107}{3805}+\dfrac{13}{8}-\dfrac{18}{5}\times\left(-3\right)\times7\\&=&\dfrac{81107}{3805}+\dfrac{13}{8}-\left(-\dfrac{54}{5}\right)\times7\\&=&\dfrac{81107}{3805}+\dfrac{13}{8}+\dfrac{378}{5}\\&=&\dfrac{698321}{30440}+\dfrac{378}{5}\\&=&\dfrac{599917}{6088}\\
\end{eqnarray*}