L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[-\dfrac{59}{8}+\dfrac{77}{3}\times\left(-9\right)+\dfrac{\dfrac{\dfrac{-\dfrac{47}{4}+\dfrac{77}{3}+0}{8}}{\dfrac{37}{3}}-\dfrac{37}{3}}{\dfrac{\dfrac{3}{-\dfrac{47}{4}}}{\left(-9\right)\times\dfrac{37}{3}\times1-\dfrac{59}{8}}}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=-\dfrac{59}{8}+\dfrac{77}{3}\times\left(-9\right)+\dfrac{\dfrac{\dfrac{-\dfrac{47}{4}+\dfrac{77}{3}+0}{8}}{\dfrac{37}{3}}-\dfrac{37}{3}}{\dfrac{\dfrac{3}{-\dfrac{47}{4}}}{\left(-9\right)\times\dfrac{37}{3}\times1-\dfrac{59}{8}}}=-\dfrac{16070681848}{2727936}\) . Voici le détail :
\begin{eqnarray*}
X &=&-\dfrac{59}{8}+\dfrac{77}{3}\times\left(-9\right)+\dfrac{\dfrac{\dfrac{\dfrac{167}{12}+0}{8}}{\dfrac{37}{3}}-\dfrac{37}{3}}{\dfrac{\dfrac{3}{-\dfrac{47}{4}}}{\left(-9\right)\times\dfrac{37}{3}\times1-\dfrac{59}{8}}}\\&=&-\dfrac{59}{8}+\dfrac{77}{3}\times\left(-9\right)+\dfrac{\dfrac{\dfrac{\dfrac{167}{12}}{8}}{\dfrac{37}{3}}-\dfrac{37}{3}}{\dfrac{\dfrac{3}{-\dfrac{47}{4}}}{\left(-9\right)\times\dfrac{37}{3}\times1-\dfrac{59}{8}}}\\&=&-\dfrac{59}{8}+\dfrac{77}{3}\times\left(-9\right)+\dfrac{\dfrac{\dfrac{\dfrac{167}{12}}{8}}{\dfrac{37}{3}}-\dfrac{37}{3}}{\dfrac{\dfrac{3}{-\dfrac{47}{4}}}{\left(-111\right)\times1-\dfrac{59}{8}}}\\&=&-\dfrac{59}{8}+\dfrac{77}{3}\times\left(-9\right)+\dfrac{\dfrac{\dfrac{\dfrac{167}{12}}{8}}{\dfrac{37}{3}}-\dfrac{37}{3}}{\dfrac{\dfrac{3}{-\dfrac{47}{4}}}{-111-\dfrac{59}{8}}}\\&=&-\dfrac{59}{8}+\dfrac{77}{3}\times\left(-9\right)+\dfrac{\dfrac{\dfrac{167}{96}}{\dfrac{37}{3}}-\dfrac{37}{3}}{\dfrac{\dfrac{3}{-\dfrac{47}{4}}}{-111-\dfrac{59}{8}}}\\&=&-\dfrac{59}{8}+\dfrac{77}{3}\times\left(-9\right)+\dfrac{\dfrac{167}{1184}-\dfrac{37}{3}}{\dfrac{\dfrac{3}{-\dfrac{47}{4}}}{-111-\dfrac{59}{8}}}\\&=&-\dfrac{59}{8}+\dfrac{77}{3}\times\left(-9\right)+\dfrac{\dfrac{167}{1184}-\dfrac{37}{3}}{\dfrac{\dfrac{3}{-\dfrac{47}{4}}}{-\dfrac{947}{8}}}\\&=&-\dfrac{59}{8}+\dfrac{77}{3}\times\left(-9\right)+\dfrac{-\dfrac{43307}{3552}}{\dfrac{\dfrac{3}{-\dfrac{47}{4}}}{-\dfrac{947}{8}}}\\&=&-\dfrac{59}{8}+\dfrac{77}{3}\times\left(-9\right)+\dfrac{-\dfrac{43307}{3552}}{\dfrac{-\dfrac{12}{47}}{-\dfrac{947}{8}}}\\&=&-\dfrac{59}{8}+\dfrac{77}{3}\times\left(-9\right)+\dfrac{-\dfrac{43307}{3552}}{\dfrac{96}{44509}}\\&=&-\dfrac{59}{8}-231+\dfrac{-\dfrac{43307}{3552}}{\dfrac{96}{44509}}\\&=&-\dfrac{59}{8}-231-\dfrac{1927551263}{340992}\\&=&-\dfrac{1907}{8}-\dfrac{1927551263}{340992}\\&=&-\dfrac{16070681848}{2727936}\\
\end{eqnarray*}