L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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Exercice
Calculer \[\left(1+\dfrac{100}{11}\right)\times\dfrac{\left(-\dfrac{124}{5}\right)\times2\times2}{\left(4-4\right)-\left(\dfrac{137}{8}+12-\dfrac{137}{8}\right)-\dfrac{\dfrac{-\dfrac{69}{2}}{7}}{-\dfrac{69}{2}}}+\dfrac{42}{11}\]
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Exercice
On a \( X=\left(1+\dfrac{100}{11}\right)\times\dfrac{\left(-\dfrac{124}{5}\right)\times2\times2}{\left(4-4\right)-\left(\dfrac{137}{8}+12-\dfrac{137}{8}\right)-\dfrac{\dfrac{-\dfrac{69}{2}}{7}}{-\dfrac{69}{2}}}+\dfrac{42}{11}=\dfrac{403242}{4675}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(1+\dfrac{100}{11}\right)\times\dfrac{\left(-\dfrac{124}{5}\right)\times2\times2}{0-\left(\dfrac{137}{8}+12-\dfrac{137}{8}\right)-\dfrac{\dfrac{-\dfrac{69}{2}}{7}}{-\dfrac{69}{2}}}+\dfrac{42}{11}\\&=&\left(1+\dfrac{100}{11}\right)\times\dfrac{\left(-\dfrac{124}{5}\right)\times2\times2}{0-\left(\dfrac{233}{8}-\dfrac{137}{8}\right)-\dfrac{\dfrac{-\dfrac{69}{2}}{7}}{-\dfrac{69}{2}}}+\dfrac{42}{11}\\&=&\left(1+\dfrac{100}{11}\right)\times\dfrac{\left(-\dfrac{124}{5}\right)\times2\times2}{0-12-\dfrac{\dfrac{-\dfrac{69}{2}}{7}}{-\dfrac{69}{2}}}+\dfrac{42}{11}\\&=&\left(1+\dfrac{100}{11}\right)\times\dfrac{\left(-\dfrac{124}{5}\right)\times2\times2}{0-12-\dfrac{-\dfrac{69}{14}}{-\dfrac{69}{2}}}+\dfrac{42}{11}\\&=&\left(1+\dfrac{100}{11}\right)\times\dfrac{\left(-\dfrac{124}{5}\right)\times2\times2}{0-12-\dfrac{1}{7}}+\dfrac{42}{11}\\&=&\left(1+\dfrac{100}{11}\right)\times\dfrac{\left(-\dfrac{248}{5}\right)\times2}{0-12-\dfrac{1}{7}}+\dfrac{42}{11}\\&=&\left(1+\dfrac{100}{11}\right)\times\dfrac{-\dfrac{496}{5}}{0-12-\dfrac{1}{7}}+\dfrac{42}{11}\\&=&\left(1+\dfrac{100}{11}\right)\times\dfrac{-\dfrac{496}{5}}{-12-\dfrac{1}{7}}+\dfrac{42}{11}\\&=&\left(1+\dfrac{100}{11}\right)\times\dfrac{-\dfrac{496}{5}}{-\dfrac{85}{7}}+\dfrac{42}{11}\\&=&\dfrac{111}{11}\times\dfrac{-\dfrac{496}{5}}{-\dfrac{85}{7}}+\dfrac{42}{11}\\&=&\dfrac{111}{11}\times\left(\dfrac{3472}{425}\right)+\dfrac{42}{11}\\&=&\dfrac{385392}{4675}+\dfrac{42}{11}\\&=&\dfrac{403242}{4675}\\
\end{eqnarray*}