L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\left(\dfrac{71}{6}+\dfrac{47}{4}-1+\dfrac{53}{3}+\dfrac{47}{4}\times\dfrac{6}{11}\times\dfrac{71}{6}\times\dfrac{53}{3}\times12+1+3-\dfrac{61}{5}\right)-\dfrac{-8}{\dfrac{91}{3}}\]
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Exercice
On a \( X=\left(\dfrac{71}{6}+\dfrac{47}{4}-1+\dfrac{53}{3}+\dfrac{47}{4}\times\dfrac{6}{11}\times\dfrac{71}{6}\times\dfrac{53}{3}\times12+1+3-\dfrac{61}{5}\right)-\dfrac{-8}{\dfrac{91}{3}}=\dfrac{322533941}{20020}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(\dfrac{71}{6}+\dfrac{47}{4}-1+\dfrac{53}{3}+\dfrac{47}{4}\times\dfrac{71}{11}\times\dfrac{53}{3}\times12+1+3-\dfrac{61}{5}\right)-\dfrac{-8}{\dfrac{91}{3}}\\&=&\left(\dfrac{71}{6}+\dfrac{47}{4}-1+\dfrac{53}{3}+\dfrac{47}{4}\times\dfrac{3763}{33}\times12+1+3-\dfrac{61}{5}\right)-\dfrac{-8}{\dfrac{91}{3}}\\&=&\left(\dfrac{71}{6}+\dfrac{47}{4}-1+\dfrac{53}{3}+\dfrac{176861}{132}\times12+1+3-\dfrac{61}{5}\right)-\dfrac{-8}{\dfrac{91}{3}}\\&=&\left(\dfrac{71}{6}+\dfrac{47}{4}-1+\dfrac{53}{3}+\dfrac{176861}{11}+1+3-\dfrac{61}{5}\right)-\dfrac{-8}{\dfrac{91}{3}}\\&=&\left(\dfrac{71}{6}+\dfrac{47}{4}-1+\dfrac{53}{3}+\dfrac{176861}{11}+1-\dfrac{46}{5}\right)-\dfrac{-8}{\dfrac{91}{3}}\\&=&\left(\dfrac{71}{6}+\dfrac{43}{4}+\dfrac{53}{3}+\dfrac{176861}{11}+1-\dfrac{46}{5}\right)-\dfrac{-8}{\dfrac{91}{3}}\\&=&\left(\dfrac{71}{6}+\dfrac{43}{4}+\dfrac{53}{3}+\dfrac{176872}{11}-\dfrac{46}{5}\right)-\dfrac{-8}{\dfrac{91}{3}}\\&=&\left(\dfrac{71}{6}+\dfrac{43}{4}+\dfrac{53}{3}+\dfrac{883854}{55}\right)-\dfrac{-8}{\dfrac{91}{3}}\\&=&\left(\dfrac{271}{12}+\dfrac{53}{3}+\dfrac{883854}{55}\right)-\dfrac{-8}{\dfrac{91}{3}}\\&=&\left(\dfrac{161}{4}+\dfrac{883854}{55}\right)-\dfrac{-8}{\dfrac{91}{3}}\\&=&\dfrac{3544271}{220}-\dfrac{-8}{\dfrac{91}{3}}\\&=&\dfrac{3544271}{220}+\dfrac{24}{91}\\&=&\dfrac{322533941}{20020}\\
\end{eqnarray*}