L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\left(-\dfrac{5}{3}\right)\times\dfrac{\dfrac{\dfrac{-5}{-\dfrac{13}{7}}}{\dfrac{\left(-5\right)\times\left(-\dfrac{5}{3}\right)}{-8}}}{-4}\times\dfrac{41}{6}\times\left(-\dfrac{5}{3}-1-\left(\dfrac{\dfrac{\dfrac{100}{7}}{\dfrac{100}{7}}}{-5}+\dfrac{43}{3}\right)\right)\times\left(-\dfrac{5}{3}\right)\times\left(-\dfrac{37}{10}\right)\times1\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\left(-\dfrac{5}{3}\right)\times\dfrac{\dfrac{\dfrac{-5}{-\dfrac{13}{7}}}{\dfrac{\left(-5\right)\times\left(-\dfrac{5}{3}\right)}{-8}}}{-4}\times\dfrac{41}{6}\times\left(-\dfrac{5}{3}-1-\left(\dfrac{\dfrac{\dfrac{100}{7}}{\dfrac{100}{7}}}{-5}+\dfrac{43}{3}\right)\right)\times\left(-\dfrac{5}{3}\right)\times\left(-\dfrac{37}{10}\right)\times1=\dfrac{148666}{195}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(-\dfrac{5}{3}\right)\times\dfrac{\dfrac{\dfrac{-5}{-\dfrac{13}{7}}}{\dfrac{\dfrac{25}{3}}{-8}}}{-4}\times\dfrac{41}{6}\times\left(-\dfrac{5}{3}-1-\left(\dfrac{\dfrac{\dfrac{100}{7}}{\dfrac{100}{7}}}{-5}+\dfrac{43}{3}\right)\right)\times\left(-\dfrac{5}{3}\right)\times\left(-\dfrac{37}{10}\right)\times1\\&=&\left(-\dfrac{5}{3}\right)\times\dfrac{\dfrac{\dfrac{-5}{-\dfrac{13}{7}}}{\dfrac{\dfrac{25}{3}}{-8}}}{-4}\times\dfrac{41}{6}\times\left(-\dfrac{5}{3}-1-\left(\dfrac{1}{-5}+\dfrac{43}{3}\right)\right)\times\left(-\dfrac{5}{3}\right)\times\left(-\dfrac{37}{10}\right)\times1\\&=&\left(-\dfrac{5}{3}\right)\times\dfrac{\dfrac{\dfrac{-5}{-\dfrac{13}{7}}}{\dfrac{\dfrac{25}{3}}{-8}}}{-4}\times\dfrac{41}{6}\times\left(-\dfrac{5}{3}-1-\left(-\dfrac{1}{5}+\dfrac{43}{3}\right)\right)\times\left(-\dfrac{5}{3}\right)\times\left(-\dfrac{37}{10}\right)\times1\\&=&\left(-\dfrac{5}{3}\right)\times\dfrac{\dfrac{\dfrac{-5}{-\dfrac{13}{7}}}{-\dfrac{25}{24}}}{-4}\times\dfrac{41}{6}\times\left(-\dfrac{5}{3}-1-\left(-\dfrac{1}{5}+\dfrac{43}{3}\right)\right)\times\left(-\dfrac{5}{3}\right)\times\left(-\dfrac{37}{10}\right)\times1\\&=&\left(-\dfrac{5}{3}\right)\times\dfrac{\dfrac{\dfrac{-5}{-\dfrac{13}{7}}}{-\dfrac{25}{24}}}{-4}\times\dfrac{41}{6}\times\left(-\dfrac{5}{3}-1-\dfrac{212}{15}\right)\times\left(-\dfrac{5}{3}\right)\times\left(-\dfrac{37}{10}\right)\times1\\&=&\left(-\dfrac{5}{3}\right)\times\dfrac{\dfrac{\dfrac{35}{13}}{-\dfrac{25}{24}}}{-4}\times\dfrac{41}{6}\times\left(-\dfrac{5}{3}-1-\dfrac{212}{15}\right)\times\left(-\dfrac{5}{3}\right)\times\left(-\dfrac{37}{10}\right)\times1\\&=&\left(-\dfrac{5}{3}\right)\times\dfrac{-\dfrac{168}{65}}{-4}\times\dfrac{41}{6}\times\left(-\dfrac{5}{3}-1-\dfrac{212}{15}\right)\times\left(-\dfrac{5}{3}\right)\times\left(-\dfrac{37}{10}\right)\times1\\&=&\left(-\dfrac{5}{3}\right)\times\dfrac{42}{65}\times\dfrac{41}{6}\times\left(-\dfrac{5}{3}-1-\dfrac{212}{15}\right)\times\left(-\dfrac{5}{3}\right)\times\left(-\dfrac{37}{10}\right)\times1\\&=&\left(-\dfrac{5}{3}\right)\times\dfrac{42}{65}\times\dfrac{41}{6}\times\left(-\dfrac{8}{3}-\dfrac{212}{15}\right)\times\left(-\dfrac{5}{3}\right)\times\left(-\dfrac{37}{10}\right)\times1\\&=&\left(-\dfrac{5}{3}\right)\times\dfrac{42}{65}\times\dfrac{41}{6}\times\left(-\dfrac{84}{5}\right)\times\left(-\dfrac{5}{3}\right)\times\left(-\dfrac{37}{10}\right)\times1\\&=&\left(-\dfrac{5}{3}\right)\times\dfrac{287}{65}\times\left(-\dfrac{84}{5}\right)\times\left(-\dfrac{5}{3}\right)\times\left(-\dfrac{37}{10}\right)\times1\\&=&\left(-\dfrac{5}{3}\right)\times\left(-\dfrac{24108}{325}\right)\times\left(-\dfrac{5}{3}\right)\times\left(-\dfrac{37}{10}\right)\times1\\&=&\left(-\dfrac{5}{3}\right)\times\dfrac{8036}{65}\times\left(-\dfrac{37}{10}\right)\times1\\&=&\left(-\dfrac{8036}{39}\right)\times\left(-\dfrac{37}{10}\right)\times1\\&=&\dfrac{148666}{195}\times1\\&=&\dfrac{148666}{195}\\
\end{eqnarray*}