L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\dfrac{143}{12}\times\left(\left(\dfrac{\dfrac{\dfrac{2}{-12}}{-\dfrac{84}{5}}}{-3}+9\right)-\dfrac{6}{7}+\dfrac{10}{3}-\dfrac{\dfrac{\dfrac{-\dfrac{68}{5}}{-12}}{-12}}{-12-\dfrac{143}{12}+\dfrac{10}{3}-\dfrac{143}{12}}\right)-12+\dfrac{6}{7}+9\]
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Exercice
On a \( X=\dfrac{143}{12}\times\left(\left(\dfrac{\dfrac{\dfrac{2}{-12}}{-\dfrac{84}{5}}}{-3}+9\right)-\dfrac{6}{7}+\dfrac{10}{3}-\dfrac{\dfrac{\dfrac{-\dfrac{68}{5}}{-12}}{-12}}{-12-\dfrac{143}{12}+\dfrac{10}{3}-\dfrac{143}{12}}\right)-12+\dfrac{6}{7}+9=\dfrac{61027817}{453600}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{143}{12}\times\left(\left(\dfrac{\dfrac{-\dfrac{1}{6}}{-\dfrac{84}{5}}}{-3}+9\right)-\dfrac{6}{7}+\dfrac{10}{3}-\dfrac{\dfrac{\dfrac{-\dfrac{68}{5}}{-12}}{-12}}{-12-\dfrac{143}{12}+\dfrac{10}{3}-\dfrac{143}{12}}\right)-12+\dfrac{6}{7}+9\\&=&\dfrac{143}{12}\times\left(\left(\dfrac{\dfrac{5}{504}}{-3}+9\right)-\dfrac{6}{7}+\dfrac{10}{3}-\dfrac{\dfrac{\dfrac{-\dfrac{68}{5}}{-12}}{-12}}{-12-\dfrac{143}{12}+\dfrac{10}{3}-\dfrac{143}{12}}\right)-12+\dfrac{6}{7}+9\\&=&\dfrac{143}{12}\times\left(\left(-\dfrac{5}{1512}+9\right)-\dfrac{6}{7}+\dfrac{10}{3}-\dfrac{\dfrac{\dfrac{-\dfrac{68}{5}}{-12}}{-12}}{-12-\dfrac{143}{12}+\dfrac{10}{3}-\dfrac{143}{12}}\right)-12+\dfrac{6}{7}+9\\&=&\dfrac{143}{12}\times\left(\left(-\dfrac{5}{1512}+9\right)-\dfrac{6}{7}+\dfrac{10}{3}-\dfrac{\dfrac{\dfrac{-\dfrac{68}{5}}{-12}}{-12}}{-\dfrac{287}{12}+\dfrac{10}{3}-\dfrac{143}{12}}\right)-12+\dfrac{6}{7}+9\\&=&\dfrac{143}{12}\times\left(\left(-\dfrac{5}{1512}+9\right)-\dfrac{6}{7}+\dfrac{10}{3}-\dfrac{\dfrac{\dfrac{-\dfrac{68}{5}}{-12}}{-12}}{-\dfrac{247}{12}-\dfrac{143}{12}}\right)-12+\dfrac{6}{7}+9\\&=&\dfrac{143}{12}\times\left(\left(-\dfrac{5}{1512}+9\right)-\dfrac{6}{7}+\dfrac{10}{3}-\dfrac{\dfrac{\dfrac{-\dfrac{68}{5}}{-12}}{-12}}{-\dfrac{65}{2}}\right)-12+\dfrac{6}{7}+9\\&=&\dfrac{143}{12}\times\left(\dfrac{13603}{1512}-\dfrac{6}{7}+\dfrac{10}{3}-\dfrac{\dfrac{\dfrac{-\dfrac{68}{5}}{-12}}{-12}}{-\dfrac{65}{2}}\right)-12+\dfrac{6}{7}+9\\&=&\dfrac{143}{12}\times\left(\dfrac{13603}{1512}-\dfrac{6}{7}+\dfrac{10}{3}-\dfrac{\dfrac{\dfrac{17}{15}}{-12}}{-\dfrac{65}{2}}\right)-12+\dfrac{6}{7}+9\\&=&\dfrac{143}{12}\times\left(\dfrac{13603}{1512}-\dfrac{6}{7}+\dfrac{10}{3}-\dfrac{-\dfrac{17}{180}}{-\dfrac{65}{2}}\right)-12+\dfrac{6}{7}+9\\&=&\dfrac{143}{12}\times\left(\dfrac{13603}{1512}-\dfrac{6}{7}+\dfrac{10}{3}-\dfrac{17}{5850}\right)-12+\dfrac{6}{7}+9\\&=&\dfrac{143}{12}\times\left(\dfrac{12307}{1512}+\dfrac{10}{3}-\dfrac{17}{5850}\right)-12+\dfrac{6}{7}+9\\&=&\dfrac{143}{12}\times\left(\dfrac{17347}{1512}-\dfrac{17}{5850}\right)-12+\dfrac{6}{7}+9\\&=&\dfrac{143}{12}\times\dfrac{5636347}{491400}-12+\dfrac{6}{7}+9\\&=&\dfrac{61999817}{453600}-12+\dfrac{6}{7}+9\\&=&\dfrac{61999817}{453600}-\dfrac{78}{7}+9\\&=&\dfrac{56945417}{453600}+9\\&=&\dfrac{61027817}{453600}\\
\end{eqnarray*}