L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[-11+11-\dfrac{\dfrac{-\dfrac{59}{4}}{-8}}{-\dfrac{22}{3}-\dfrac{75}{7}-\left(\dfrac{28}{9}+\dfrac{\dfrac{-11}{5}}{-\dfrac{59}{4}}\right)-\left(-6-6-6-\dfrac{22}{3}-\dfrac{59}{4}-6\right)}-\left(-\dfrac{59}{4}-5+11\right)\]
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Exercice
On a \( X=-11+11-\dfrac{\dfrac{-\dfrac{59}{4}}{-8}}{-\dfrac{22}{3}-\dfrac{75}{7}-\left(\dfrac{28}{9}+\dfrac{\dfrac{-11}{5}}{-\dfrac{59}{4}}\right)-\left(-6-6-6-\dfrac{22}{3}-\dfrac{59}{4}-6\right)}-\left(-\dfrac{59}{4}-5+11\right)=\dfrac{127829975}{14734456}\) . Voici le détail :
\begin{eqnarray*}
X &=&-11+11-\dfrac{\dfrac{-\dfrac{59}{4}}{-8}}{-\dfrac{22}{3}-\dfrac{75}{7}-\left(\dfrac{28}{9}+\dfrac{-\dfrac{11}{5}}{-\dfrac{59}{4}}\right)-\left(-6-6-6-\dfrac{22}{3}-\dfrac{59}{4}-6\right)}-\left(-\dfrac{59}{4}-5+11\right)\\&=&-11+11-\dfrac{\dfrac{-\dfrac{59}{4}}{-8}}{-\dfrac{22}{3}-\dfrac{75}{7}-\left(\dfrac{28}{9}+\dfrac{44}{295}\right)-\left(-6-6-6-\dfrac{22}{3}-\dfrac{59}{4}-6\right)}-\left(-\dfrac{59}{4}-5+11\right)\\&=&-11+11-\dfrac{\dfrac{-\dfrac{59}{4}}{-8}}{-\dfrac{22}{3}-\dfrac{75}{7}-\left(\dfrac{28}{9}+\dfrac{44}{295}\right)-\left(-12-6-\dfrac{22}{3}-\dfrac{59}{4}-6\right)}-\left(-\dfrac{59}{4}-5+11\right)\\&=&-11+11-\dfrac{\dfrac{-\dfrac{59}{4}}{-8}}{-\dfrac{22}{3}-\dfrac{75}{7}-\left(\dfrac{28}{9}+\dfrac{44}{295}\right)-\left(-18-\dfrac{22}{3}-\dfrac{59}{4}-6\right)}-\left(-\dfrac{59}{4}-5+11\right)\\&=&-11+11-\dfrac{\dfrac{-\dfrac{59}{4}}{-8}}{-\dfrac{22}{3}-\dfrac{75}{7}-\left(\dfrac{28}{9}+\dfrac{44}{295}\right)-\left(-\dfrac{76}{3}-\dfrac{59}{4}-6\right)}-\left(-\dfrac{59}{4}-5+11\right)\\&=&-11+11-\dfrac{\dfrac{-\dfrac{59}{4}}{-8}}{-\dfrac{22}{3}-\dfrac{75}{7}-\dfrac{8656}{2655}-\left(-\dfrac{76}{3}-\dfrac{59}{4}-6\right)}-\left(-\dfrac{59}{4}-5+11\right)\\&=&-11+11-\dfrac{\dfrac{-\dfrac{59}{4}}{-8}}{-\dfrac{22}{3}-\dfrac{75}{7}-\dfrac{8656}{2655}-\left(-\dfrac{481}{12}-6\right)}-\left(-\dfrac{59}{4}-5+11\right)\\&=&-11+11-\dfrac{\dfrac{-\dfrac{59}{4}}{-8}}{-\dfrac{22}{3}-\dfrac{75}{7}-\dfrac{8656}{2655}+\dfrac{553}{12}}-\left(-\dfrac{59}{4}-5+11\right)\\&=&-11+11-\dfrac{\dfrac{-\dfrac{59}{4}}{-8}}{-\dfrac{379}{21}-\dfrac{8656}{2655}+\dfrac{553}{12}}-\left(-\dfrac{59}{4}-5+11\right)\\&=&-11+11-\dfrac{\dfrac{-\dfrac{59}{4}}{-8}}{-\dfrac{396007}{18585}+\dfrac{553}{12}}-\left(-\dfrac{59}{4}-5+11\right)\\&=&-11+11-\dfrac{\dfrac{-\dfrac{59}{4}}{-8}}{\dfrac{1841807}{74340}}-\left(-\dfrac{59}{4}-5+11\right)\\&=&-11+11-\dfrac{\dfrac{59}{32}}{\dfrac{1841807}{74340}}-\left(-\dfrac{59}{4}-5+11\right)\\&=&-11+11-\dfrac{1096515}{14734456}-\left(-\dfrac{59}{4}-5+11\right)\\&=&-11+11-\dfrac{1096515}{14734456}-\left(-\dfrac{79}{4}+11\right)\\&=&-11+11-\dfrac{1096515}{14734456}+\dfrac{35}{4}\\&=&0-\dfrac{1096515}{14734456}+\dfrac{35}{4}\\&=&-\dfrac{1096515}{14734456}+\dfrac{35}{4}\\&=&\dfrac{127829975}{14734456}\\
\end{eqnarray*}