L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\dfrac{\dfrac{\dfrac{53}{2}}{-\dfrac{103}{7}}}{\left(\left(-5-\dfrac{35}{3}+\dfrac{103}{7}\right)+\dfrac{46}{9}+\dfrac{46}{9}\right)\times11\times\dfrac{\dfrac{35}{3}}{\left(-\dfrac{103}{7}\right)\times\left(-\dfrac{103}{7}\right)}\times\left(-5-6\right)}\]
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Exercice
On a \( X=\dfrac{\dfrac{\dfrac{53}{2}}{-\dfrac{103}{7}}}{\left(\left(-5-\dfrac{35}{3}+\dfrac{103}{7}\right)+\dfrac{46}{9}+\dfrac{46}{9}\right)\times11\times\dfrac{\dfrac{35}{3}}{\left(-\dfrac{103}{7}\right)\times\left(-\dfrac{103}{7}\right)}\times\left(-5-6\right)}=\dfrac{106270353}{3181679270}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{\dfrac{53}{2}}{-\dfrac{103}{7}}}{\left(\left(-\dfrac{50}{3}+\dfrac{103}{7}\right)+\dfrac{46}{9}+\dfrac{46}{9}\right)\times11\times\dfrac{\dfrac{35}{3}}{\left(-\dfrac{103}{7}\right)\times\left(-\dfrac{103}{7}\right)}\times\left(-5-6\right)}\\&=&\dfrac{\dfrac{\dfrac{53}{2}}{-\dfrac{103}{7}}}{\left(-\dfrac{41}{21}+\dfrac{46}{9}+\dfrac{46}{9}\right)\times11\times\dfrac{\dfrac{35}{3}}{\left(-\dfrac{103}{7}\right)\times\left(-\dfrac{103}{7}\right)}\times\left(-5-6\right)}\\&=&\dfrac{\dfrac{\dfrac{53}{2}}{-\dfrac{103}{7}}}{\left(-\dfrac{41}{21}+\dfrac{46}{9}+\dfrac{46}{9}\right)\times11\times\dfrac{\dfrac{35}{3}}{\dfrac{10609}{49}}\times\left(-5-6\right)}\\&=&\dfrac{\dfrac{\dfrac{53}{2}}{-\dfrac{103}{7}}}{\left(\dfrac{199}{63}+\dfrac{46}{9}\right)\times11\times\dfrac{\dfrac{35}{3}}{\dfrac{10609}{49}}\times\left(-5-6\right)}\\&=&\dfrac{\dfrac{\dfrac{53}{2}}{-\dfrac{103}{7}}}{\dfrac{521}{63}\times11\times\dfrac{\dfrac{35}{3}}{\dfrac{10609}{49}}\times\left(-5-6\right)}\\&=&\dfrac{\dfrac{\dfrac{53}{2}}{-\dfrac{103}{7}}}{\dfrac{521}{63}\times11\times\dfrac{1715}{31827}\times\left(-5-6\right)}\\&=&\dfrac{\dfrac{\dfrac{53}{2}}{-\dfrac{103}{7}}}{\dfrac{521}{63}\times11\times\dfrac{1715}{31827}\times-11}\\&=&\dfrac{\dfrac{\dfrac{53}{2}}{-\dfrac{103}{7}}}{\dfrac{5731}{63}\times\dfrac{1715}{31827}\times-11}\\&=&\dfrac{\dfrac{\dfrac{53}{2}}{-\dfrac{103}{7}}}{\dfrac{1404095}{286443}\times-11}\\&=&\dfrac{\dfrac{\dfrac{53}{2}}{-\dfrac{103}{7}}}{-\dfrac{15445045}{286443}}\\&=&\dfrac{-\dfrac{371}{206}}{-\dfrac{15445045}{286443}}\\&=&\dfrac{106270353}{3181679270}\\
\end{eqnarray*}