L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\dfrac{\dfrac{\dfrac{\dfrac{35}{3}}{\left(-8\right)\times\dfrac{5}{8}\times\left(7-8+\dfrac{5}{8}+2+\dfrac{\dfrac{\dfrac{\dfrac{59}{2}+5+\dfrac{59}{2}}{-2}}{3}}{-2}\right)\times\left(\dfrac{7}{11}-4+\dfrac{\dfrac{35}{3}\times6\times\left(-10\right)\times\left(-4\right)}{6}\right)}}{\dfrac{5}{8}}}{\dfrac{5}{8}}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{\dfrac{\dfrac{\dfrac{35}{3}}{\left(-8\right)\times\dfrac{5}{8}\times\left(7-8+\dfrac{5}{8}+2+\dfrac{\dfrac{\dfrac{\dfrac{59}{2}+5+\dfrac{59}{2}}{-2}}{3}}{-2}\right)\times\left(\dfrac{7}{11}-4+\dfrac{\dfrac{35}{3}\times6\times\left(-10\right)\times\left(-4\right)}{6}\right)}}{\dfrac{5}{8}}}{\dfrac{5}{8}}=-\dfrac{118272}{63831575}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{\dfrac{\dfrac{35}{3}}{\left(-8\right)\times\dfrac{5}{8}\times\left(7-8+\dfrac{5}{8}+2+\dfrac{\dfrac{\dfrac{\dfrac{69}{2}+\dfrac{59}{2}}{-2}}{3}}{-2}\right)\times\left(\dfrac{7}{11}-4+\dfrac{\dfrac{35}{3}\times6\times\left(-10\right)\times\left(-4\right)}{6}\right)}}{\dfrac{5}{8}}}{\dfrac{5}{8}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{35}{3}}{\left(-8\right)\times\dfrac{5}{8}\times\left(7-8+\dfrac{5}{8}+2+\dfrac{\dfrac{\dfrac{64}{-2}}{3}}{-2}\right)\times\left(\dfrac{7}{11}-4+\dfrac{\dfrac{35}{3}\times6\times\left(-10\right)\times\left(-4\right)}{6}\right)}}{\dfrac{5}{8}}}{\dfrac{5}{8}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{35}{3}}{\left(-8\right)\times\dfrac{5}{8}\times\left(7-8+\dfrac{5}{8}+2+\dfrac{\dfrac{\dfrac{64}{-2}}{3}}{-2}\right)\times\left(\dfrac{7}{11}-4+\dfrac{70\times\left(-10\right)\times\left(-4\right)}{6}\right)}}{\dfrac{5}{8}}}{\dfrac{5}{8}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{35}{3}}{\left(-8\right)\times\dfrac{5}{8}\times\left(7-8+\dfrac{5}{8}+2+\dfrac{\dfrac{\dfrac{64}{-2}}{3}}{-2}\right)\times\left(\dfrac{7}{11}-4+\dfrac{\left(-700\right)\times\left(-4\right)}{6}\right)}}{\dfrac{5}{8}}}{\dfrac{5}{8}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{35}{3}}{\left(-8\right)\times\dfrac{5}{8}\times\left(7-8+\dfrac{5}{8}+2+\dfrac{\dfrac{\dfrac{64}{-2}}{3}}{-2}\right)\times\left(\dfrac{7}{11}-4+\dfrac{2800}{6}\right)}}{\dfrac{5}{8}}}{\dfrac{5}{8}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{35}{3}}{\left(-8\right)\times\dfrac{5}{8}\times\left(7-8+\dfrac{21}{8}+\dfrac{\dfrac{\dfrac{64}{-2}}{3}}{-2}\right)\times\left(\dfrac{7}{11}-4+\dfrac{2800}{6}\right)}}{\dfrac{5}{8}}}{\dfrac{5}{8}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{35}{3}}{\left(-8\right)\times\dfrac{5}{8}\times\left(7-8+\dfrac{21}{8}+\dfrac{\dfrac{-32}{3}}{-2}\right)\times\left(\dfrac{7}{11}-4+\dfrac{2800}{6}\right)}}{\dfrac{5}{8}}}{\dfrac{5}{8}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{35}{3}}{\left(-8\right)\times\dfrac{5}{8}\times\left(7-8+\dfrac{21}{8}+\dfrac{-\dfrac{32}{3}}{-2}\right)\times\left(\dfrac{7}{11}-4+\dfrac{2800}{6}\right)}}{\dfrac{5}{8}}}{\dfrac{5}{8}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{35}{3}}{\left(-8\right)\times\dfrac{5}{8}\times\left(7-8+\dfrac{21}{8}+\dfrac{16}{3}\right)\times\left(\dfrac{7}{11}-4+\dfrac{2800}{6}\right)}}{\dfrac{5}{8}}}{\dfrac{5}{8}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{35}{3}}{\left(-8\right)\times\dfrac{5}{8}\times\left(7-8+\dfrac{21}{8}+\dfrac{16}{3}\right)\times\left(\dfrac{7}{11}-4+\dfrac{2800}{6}\right)}}{\dfrac{5}{8}}}{\dfrac{5}{8}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{35}{3}}{\left(-8\right)\times\dfrac{5}{8}\times\left(7-8+\dfrac{21}{8}+\dfrac{16}{3}\right)\times\left(\dfrac{7}{11}-4+\dfrac{1400}{3}\right)}}{\dfrac{5}{8}}}{\dfrac{5}{8}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{35}{3}}{\left(-8\right)\times\dfrac{5}{8}\times\left(-1+\dfrac{21}{8}+\dfrac{16}{3}\right)\times\left(\dfrac{7}{11}-4+\dfrac{1400}{3}\right)}}{\dfrac{5}{8}}}{\dfrac{5}{8}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{35}{3}}{\left(-8\right)\times\dfrac{5}{8}\times\left(\dfrac{13}{8}+\dfrac{16}{3}\right)\times\left(\dfrac{7}{11}-4+\dfrac{1400}{3}\right)}}{\dfrac{5}{8}}}{\dfrac{5}{8}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{35}{3}}{\left(-8\right)\times\dfrac{5}{8}\times\dfrac{167}{24}\times\left(\dfrac{7}{11}-4+\dfrac{1400}{3}\right)}}{\dfrac{5}{8}}}{\dfrac{5}{8}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{35}{3}}{\left(-8\right)\times\dfrac{5}{8}\times\dfrac{167}{24}\times\left(-\dfrac{37}{11}+\dfrac{1400}{3}\right)}}{\dfrac{5}{8}}}{\dfrac{5}{8}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{35}{3}}{\left(-8\right)\times\dfrac{5}{8}\times\dfrac{167}{24}\times\dfrac{15289}{33}}}{\dfrac{5}{8}}}{\dfrac{5}{8}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{35}{3}}{\left(-5\right)\times\dfrac{167}{24}\times\dfrac{15289}{33}}}{\dfrac{5}{8}}}{\dfrac{5}{8}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{35}{3}}{\left(-\dfrac{835}{24}\right)\times\dfrac{15289}{33}}}{\dfrac{5}{8}}}{\dfrac{5}{8}}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{35}{3}}{-\dfrac{12766315}{792}}}{\dfrac{5}{8}}}{\dfrac{5}{8}}\\&=&\dfrac{\dfrac{-\dfrac{1848}{2553263}}{\dfrac{5}{8}}}{\dfrac{5}{8}}\\&=&\dfrac{-\dfrac{14784}{12766315}}{\dfrac{5}{8}}\\&=&-\dfrac{118272}{63831575}\\
\end{eqnarray*}