L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[4+7+\dfrac{\dfrac{133}{11}}{7-8-12}-\dfrac{141}{7}+\dfrac{135}{4}-\dfrac{128}{3}\times8\times\dfrac{\dfrac{\dfrac{19}{12}}{-5}}{-12}+7\]
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Exercice
On a \( X=4+7+\dfrac{\dfrac{133}{11}}{7-8-12}-\dfrac{141}{7}+\dfrac{135}{4}-\dfrac{128}{3}\times8\times\dfrac{\dfrac{\dfrac{19}{12}}{-5}}{-12}+7=\dfrac{11713321}{540540}\) . Voici le détail :
\begin{eqnarray*}
X &=&4+7+\dfrac{\dfrac{133}{11}}{-1-12}-\dfrac{141}{7}+\dfrac{135}{4}-\dfrac{128}{3}\times8\times\dfrac{\dfrac{\dfrac{19}{12}}{-5}}{-12}+7\\&=&4+7+\dfrac{\dfrac{133}{11}}{-13}-\dfrac{141}{7}+\dfrac{135}{4}-\dfrac{128}{3}\times8\times\dfrac{\dfrac{\dfrac{19}{12}}{-5}}{-12}+7\\&=&4+7+\dfrac{\dfrac{133}{11}}{-13}-\dfrac{141}{7}+\dfrac{135}{4}-\dfrac{128}{3}\times8\times\dfrac{-\dfrac{19}{60}}{-12}+7\\&=&4+7+\dfrac{\dfrac{133}{11}}{-13}-\dfrac{141}{7}+\dfrac{135}{4}-\dfrac{128}{3}\times8\times\dfrac{19}{720}+7\\&=&4+7-\dfrac{133}{143}-\dfrac{141}{7}+\dfrac{135}{4}-\dfrac{128}{3}\times8\times\dfrac{19}{720}+7\\&=&4+7-\dfrac{133}{143}-\dfrac{141}{7}+\dfrac{135}{4}-\dfrac{1024}{3}\times\dfrac{19}{720}+7\\&=&4+7-\dfrac{133}{143}-\dfrac{141}{7}+\dfrac{135}{4}-\dfrac{1216}{135}+7\\&=&4+\dfrac{868}{143}-\dfrac{141}{7}+\dfrac{135}{4}-\dfrac{1216}{135}+7\\&=&4+\dfrac{868}{143}-\dfrac{141}{7}+\dfrac{13361}{540}+7\\&=&4-\dfrac{14087}{1001}+\dfrac{13361}{540}+7\\&=&4+\dfrac{5767381}{540540}+7\\&=&\dfrac{7929541}{540540}+7\\&=&\dfrac{11713321}{540540}\\
\end{eqnarray*}