L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\dfrac{\dfrac{\dfrac{-\dfrac{56}{5}}{\dfrac{106}{9}+\dfrac{140}{11}+\dfrac{140}{11}}}{-2}}{-7+7+\dfrac{121}{6}+\dfrac{1}{2}+\dfrac{7}{2}+\dfrac{\dfrac{\dfrac{\dfrac{41}{5}}{\dfrac{83}{7}}}{\dfrac{41}{5}}}{-\dfrac{109}{11}}}\times11\times4\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{\dfrac{\dfrac{-\dfrac{56}{5}}{\dfrac{106}{9}+\dfrac{140}{11}+\dfrac{140}{11}}}{-2}}{-7+7+\dfrac{121}{6}+\dfrac{1}{2}+\dfrac{7}{2}+\dfrac{\dfrac{\dfrac{\dfrac{41}{5}}{\dfrac{83}{7}}}{\dfrac{41}{5}}}{-\dfrac{109}{11}}}\times11\times4=\dfrac{3310333488}{12084117895}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{\dfrac{-\dfrac{56}{5}}{\dfrac{106}{9}+\dfrac{140}{11}+\dfrac{140}{11}}}{-2}}{-7+7+\dfrac{121}{6}+\dfrac{1}{2}+\dfrac{7}{2}+\dfrac{\dfrac{\dfrac{287}{415}}{\dfrac{41}{5}}}{-\dfrac{109}{11}}}\times11\times4\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{56}{5}}{\dfrac{106}{9}+\dfrac{140}{11}+\dfrac{140}{11}}}{-2}}{-7+7+\dfrac{121}{6}+\dfrac{1}{2}+\dfrac{7}{2}+\dfrac{\dfrac{7}{83}}{-\dfrac{109}{11}}}\times11\times4\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{56}{5}}{\dfrac{106}{9}+\dfrac{140}{11}+\dfrac{140}{11}}}{-2}}{-7+7+\dfrac{121}{6}+\dfrac{1}{2}+\dfrac{7}{2}-\dfrac{77}{9047}}\times11\times4\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{56}{5}}{\dfrac{106}{9}+\dfrac{140}{11}+\dfrac{140}{11}}}{-2}}{0+\dfrac{121}{6}+\dfrac{1}{2}+\dfrac{7}{2}-\dfrac{77}{9047}}\times11\times4\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{56}{5}}{\dfrac{106}{9}+\dfrac{140}{11}+\dfrac{140}{11}}}{-2}}{0+\dfrac{121}{6}+\dfrac{1}{2}+\dfrac{63175}{18094}}\times11\times4\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{56}{5}}{\dfrac{2426}{99}+\dfrac{140}{11}}}{-2}}{0+\dfrac{121}{6}+\dfrac{1}{2}+\dfrac{63175}{18094}}\times11\times4\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{56}{5}}{\dfrac{3686}{99}}}{-2}}{0+\dfrac{121}{6}+\dfrac{1}{2}+\dfrac{63175}{18094}}\times11\times4\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{56}{5}}{\dfrac{3686}{99}}}{-2}}{\dfrac{121}{6}+\dfrac{1}{2}+\dfrac{63175}{18094}}\times11\times4\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{56}{5}}{\dfrac{3686}{99}}}{-2}}{\dfrac{62}{3}+\dfrac{63175}{18094}}\times11\times4\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{56}{5}}{\dfrac{3686}{99}}}{-2}}{\dfrac{1311353}{54282}}\times11\times4\\&=&\dfrac{\dfrac{-\dfrac{2772}{9215}}{-2}}{\dfrac{1311353}{54282}}\times11\times4\\&=&\dfrac{\dfrac{1386}{9215}}{\dfrac{1311353}{54282}}\times11\times4\\&=&\dfrac{75234852}{12084117895}\times11\times4\\&=&\dfrac{827583372}{12084117895}\times4\\&=&\dfrac{3310333488}{12084117895}\\
\end{eqnarray*}