L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\dfrac{0}{\left(10+\dfrac{\dfrac{\dfrac{-6}{10}}{-\dfrac{15}{2}}}{-6}-\dfrac{15}{2}+1\right)-\dfrac{125}{12}-\left(10-6-\dfrac{15}{2}+9\right)\times\left(-\dfrac{141}{8}\right)}\times\dfrac{136}{5}\times0\]
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Exercice
On a \( X=\dfrac{0}{\left(10+\dfrac{\dfrac{\dfrac{-6}{10}}{-\dfrac{15}{2}}}{-6}-\dfrac{15}{2}+1\right)-\dfrac{125}{12}-\left(10-6-\dfrac{15}{2}+9\right)\times\left(-\dfrac{141}{8}\right)}\times\dfrac{136}{5}\times0=0\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{0}{\left(10+\dfrac{\dfrac{-\dfrac{3}{5}}{-\dfrac{15}{2}}}{-6}-\dfrac{15}{2}+1\right)-\dfrac{125}{12}-\left(10-6-\dfrac{15}{2}+9\right)\times\left(-\dfrac{141}{8}\right)}\times\dfrac{136}{5}\times0\\&=&\dfrac{0}{\left(10+\dfrac{\dfrac{2}{25}}{-6}-\dfrac{15}{2}+1\right)-\dfrac{125}{12}-\left(10-6-\dfrac{15}{2}+9\right)\times\left(-\dfrac{141}{8}\right)}\times\dfrac{136}{5}\times0\\&=&\dfrac{0}{\left(10-\dfrac{1}{75}-\dfrac{15}{2}+1\right)-\dfrac{125}{12}-\left(10-6-\dfrac{15}{2}+9\right)\times\left(-\dfrac{141}{8}\right)}\times\dfrac{136}{5}\times0\\&=&\dfrac{0}{\left(10-\dfrac{1}{75}-\dfrac{15}{2}+1\right)-\dfrac{125}{12}-\left(4-\dfrac{15}{2}+9\right)\times\left(-\dfrac{141}{8}\right)}\times\dfrac{136}{5}\times0\\&=&\dfrac{0}{\left(10-\dfrac{1}{75}-\dfrac{15}{2}+1\right)-\dfrac{125}{12}-\left(-\dfrac{7}{2}+9\right)\times\left(-\dfrac{141}{8}\right)}\times\dfrac{136}{5}\times0\\&=&\dfrac{0}{\left(10-\dfrac{1}{75}-\dfrac{15}{2}+1\right)-\dfrac{125}{12}-\dfrac{11}{2}\times\left(-\dfrac{141}{8}\right)}\times\dfrac{136}{5}\times0\\&=&\dfrac{0}{\left(\dfrac{749}{75}-\dfrac{15}{2}+1\right)-\dfrac{125}{12}-\dfrac{11}{2}\times\left(-\dfrac{141}{8}\right)}\times\dfrac{136}{5}\times0\\&=&\dfrac{0}{\left(\dfrac{373}{150}+1\right)-\dfrac{125}{12}-\dfrac{11}{2}\times\left(-\dfrac{141}{8}\right)}\times\dfrac{136}{5}\times0\\&=&\dfrac{0}{\dfrac{523}{150}-\dfrac{125}{12}-\dfrac{11}{2}\times\left(-\dfrac{141}{8}\right)}\times\dfrac{136}{5}\times0\\&=&\dfrac{0}{\dfrac{523}{150}-\dfrac{125}{12}+\dfrac{1551}{16}}\times\dfrac{136}{5}\times0\\&=&\dfrac{0}{-\dfrac{693}{100}+\dfrac{1551}{16}}\times\dfrac{136}{5}\times0\\&=&\dfrac{0}{\dfrac{36003}{400}}\times\dfrac{136}{5}\times0\\&=&0\times\dfrac{136}{5}\times0\\&=&0\times0\\&=&0\\
\end{eqnarray*}