L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\dfrac{\dfrac{36}{5}}{\dfrac{36}{5}+2-\left(-\dfrac{27}{11}\right)\times\left(\dfrac{99}{2}-6\right)\times\dfrac{99}{2}+\dfrac{\dfrac{\dfrac{-\dfrac{127}{12}}{11-\dfrac{110}{7}}}{-\dfrac{127}{12}}}{-1+6}}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{\dfrac{36}{5}}{\dfrac{36}{5}+2-\left(-\dfrac{27}{11}\right)\times\left(\dfrac{99}{2}-6\right)\times\dfrac{99}{2}+\dfrac{\dfrac{\dfrac{-\dfrac{127}{12}}{11-\dfrac{110}{7}}}{-\dfrac{127}{12}}}{-1+6}}=\dfrac{4752}{3494309}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{36}{5}}{\dfrac{36}{5}+2-\left(-\dfrac{27}{11}\right)\times\dfrac{87}{2}\times\dfrac{99}{2}+\dfrac{\dfrac{\dfrac{-\dfrac{127}{12}}{11-\dfrac{110}{7}}}{-\dfrac{127}{12}}}{-1+6}}\\&=&\dfrac{\dfrac{36}{5}}{\dfrac{36}{5}+2-\left(-\dfrac{27}{11}\right)\times\dfrac{87}{2}\times\dfrac{99}{2}+\dfrac{\dfrac{\dfrac{-\dfrac{127}{12}}{-\dfrac{33}{7}}}{-\dfrac{127}{12}}}{-1+6}}\\&=&\dfrac{\dfrac{36}{5}}{\dfrac{36}{5}+2-\left(-\dfrac{2349}{22}\right)\times\dfrac{99}{2}+\dfrac{\dfrac{\dfrac{-\dfrac{127}{12}}{-\dfrac{33}{7}}}{-\dfrac{127}{12}}}{-1+6}}\\&=&\dfrac{\dfrac{36}{5}}{\dfrac{36}{5}+2+\dfrac{21141}{4}+\dfrac{\dfrac{\dfrac{-\dfrac{127}{12}}{-\dfrac{33}{7}}}{-\dfrac{127}{12}}}{-1+6}}\\&=&\dfrac{\dfrac{36}{5}}{\dfrac{36}{5}+2+\dfrac{21141}{4}+\dfrac{\dfrac{\dfrac{889}{396}}{-\dfrac{127}{12}}}{-1+6}}\\&=&\dfrac{\dfrac{36}{5}}{\dfrac{36}{5}+2+\dfrac{21141}{4}+\dfrac{\dfrac{\dfrac{889}{396}}{-\dfrac{127}{12}}}{5}}\\&=&\dfrac{\dfrac{36}{5}}{\dfrac{46}{5}+\dfrac{21141}{4}+\dfrac{\dfrac{\dfrac{889}{396}}{-\dfrac{127}{12}}}{5}}\\&=&\dfrac{\dfrac{36}{5}}{\dfrac{105889}{20}+\dfrac{\dfrac{\dfrac{889}{396}}{-\dfrac{127}{12}}}{5}}\\&=&\dfrac{\dfrac{36}{5}}{\dfrac{105889}{20}+\dfrac{-\dfrac{7}{33}}{5}}\\&=&\dfrac{\dfrac{36}{5}}{\dfrac{105889}{20}-\dfrac{7}{165}}\\&=&\dfrac{\dfrac{36}{5}}{\dfrac{3494309}{660}}\\&=&\dfrac{4752}{3494309}\\
\end{eqnarray*}