L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\left(-9\right)\times\left(-\dfrac{11}{6}-1-\left(-\dfrac{143}{3}\right)\times\left(-\dfrac{5}{7}\right)\times\dfrac{9}{4}\times\left(-9\right)\times\left(-\dfrac{117}{4}\right)\times\left(-\dfrac{29}{5}\right)\times\dfrac{-\dfrac{11}{6}}{-\dfrac{5}{7}}\right)-9+\dfrac{39}{11}-5\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\left(-9\right)\times\left(-\dfrac{11}{6}-1-\left(-\dfrac{143}{3}\right)\times\left(-\dfrac{5}{7}\right)\times\dfrac{9}{4}\times\left(-9\right)\times\left(-\dfrac{117}{4}\right)\times\left(-\dfrac{29}{5}\right)\times\dfrac{-\dfrac{11}{6}}{-\dfrac{5}{7}}\right)-9+\dfrac{39}{11}-5=-\dfrac{4755408919}{1760}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(-9\right)\times\left(-\dfrac{11}{6}-1-\dfrac{715}{21}\times\dfrac{9}{4}\times\left(-9\right)\times\left(-\dfrac{117}{4}\right)\times\left(-\dfrac{29}{5}\right)\times\dfrac{-\dfrac{11}{6}}{-\dfrac{5}{7}}\right)-9+\dfrac{39}{11}-5\\&=&\left(-9\right)\times\left(-\dfrac{11}{6}-1-\dfrac{2145}{28}\times\left(-9\right)\times\left(-\dfrac{117}{4}\right)\times\left(-\dfrac{29}{5}\right)\times\dfrac{-\dfrac{11}{6}}{-\dfrac{5}{7}}\right)-9+\dfrac{39}{11}-5\\&=&\left(-9\right)\times\left(-\dfrac{11}{6}-1-\left(-\dfrac{19305}{28}\right)\times\left(-\dfrac{117}{4}\right)\times\left(-\dfrac{29}{5}\right)\times\dfrac{-\dfrac{11}{6}}{-\dfrac{5}{7}}\right)-9+\dfrac{39}{11}-5\\&=&\left(-9\right)\times\left(-\dfrac{11}{6}-1-\left(-\dfrac{19305}{28}\right)\times\dfrac{3393}{20}\times\dfrac{-\dfrac{11}{6}}{-\dfrac{5}{7}}\right)-9+\dfrac{39}{11}-5\\&=&\left(-9\right)\times\left(-\dfrac{11}{6}-1-\left(-\dfrac{19305}{28}\right)\times\dfrac{3393}{20}\times\dfrac{77}{30}\right)-9+\dfrac{39}{11}-5\\&=&\left(-9\right)\times\left(-\dfrac{11}{6}-1-\left(-\dfrac{13100373}{112}\right)\times\dfrac{77}{30}\right)-9+\dfrac{39}{11}-5\\&=&\left(-9\right)\times\left(-\dfrac{11}{6}-1+\dfrac{48034701}{160}\right)-9+\dfrac{39}{11}-5\\&=&\left(-9\right)\times\left(-\dfrac{17}{6}+\dfrac{48034701}{160}\right)-9+\dfrac{39}{11}-5\\&=&\left(-9\right)\times\dfrac{144102743}{480}-9+\dfrac{39}{11}-5\\&=&-\dfrac{432308229}{160}-9+\dfrac{39}{11}-5\\&=&-\dfrac{432309669}{160}+\dfrac{39}{11}-5\\&=&-\dfrac{4755400119}{1760}-5\\&=&-\dfrac{4755408919}{1760}\\
\end{eqnarray*}