L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\left(-9\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{86}{11}}{\dfrac{8}{7}}}{\dfrac{23}{5}-\dfrac{23}{5}-\left(\dfrac{86}{11}+\dfrac{86}{11}-\dfrac{47}{3}+\dfrac{93}{7}+\dfrac{13}{2}+5-\dfrac{135}{2}\right)+\dfrac{61}{11}}}{\dfrac{23}{5}-5-\dfrac{2}{3}-\left(-4+\dfrac{61}{11}\right)}}{\dfrac{2}{3}-5+\dfrac{61}{11}-9}\times\dfrac{86}{11}\]
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Exercice
On a \( X=\left(-9\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{86}{11}}{\dfrac{8}{7}}}{\dfrac{23}{5}-\dfrac{23}{5}-\left(\dfrac{86}{11}+\dfrac{86}{11}-\dfrac{47}{3}+\dfrac{93}{7}+\dfrac{13}{2}+5-\dfrac{135}{2}\right)+\dfrac{61}{11}}}{\dfrac{23}{5}-5-\dfrac{2}{3}-\left(-4+\dfrac{61}{11}\right)}}{\dfrac{2}{3}-5+\dfrac{61}{11}-9}\times\dfrac{86}{11}=-\dfrac{5327882406}{10873331788}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(-9\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{86}{11}}{\dfrac{8}{7}}}{\dfrac{23}{5}-\dfrac{23}{5}-\left(\dfrac{86}{11}+\dfrac{86}{11}-\dfrac{50}{21}+\dfrac{13}{2}+5-\dfrac{135}{2}\right)+\dfrac{61}{11}}}{\dfrac{23}{5}-5-\dfrac{2}{3}-\left(-4+\dfrac{61}{11}\right)}}{\dfrac{2}{3}-5+\dfrac{61}{11}-9}\times\dfrac{86}{11}\\&=&\left(-9\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{86}{11}}{\dfrac{8}{7}}}{\dfrac{23}{5}-\dfrac{23}{5}-\left(\dfrac{86}{11}+\dfrac{86}{11}+\dfrac{173}{42}+5-\dfrac{135}{2}\right)+\dfrac{61}{11}}}{\dfrac{23}{5}-5-\dfrac{2}{3}-\left(-4+\dfrac{61}{11}\right)}}{\dfrac{2}{3}-5+\dfrac{61}{11}-9}\times\dfrac{86}{11}\\&=&\left(-9\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{86}{11}}{\dfrac{8}{7}}}{\dfrac{23}{5}-\dfrac{23}{5}-\left(\dfrac{86}{11}+\dfrac{86}{11}+\dfrac{383}{42}-\dfrac{135}{2}\right)+\dfrac{61}{11}}}{\dfrac{23}{5}-5-\dfrac{2}{3}-\left(-4+\dfrac{61}{11}\right)}}{\dfrac{2}{3}-5+\dfrac{61}{11}-9}\times\dfrac{86}{11}\\&=&\left(-9\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{86}{11}}{\dfrac{8}{7}}}{\dfrac{23}{5}-\dfrac{23}{5}-\left(\dfrac{172}{11}+\dfrac{383}{42}-\dfrac{135}{2}\right)+\dfrac{61}{11}}}{\dfrac{23}{5}-5-\dfrac{2}{3}-\left(-4+\dfrac{61}{11}\right)}}{\dfrac{2}{3}-5+\dfrac{61}{11}-9}\times\dfrac{86}{11}\\&=&\left(-9\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{86}{11}}{\dfrac{8}{7}}}{\dfrac{23}{5}-\dfrac{23}{5}-\left(\dfrac{11437}{462}-\dfrac{135}{2}\right)+\dfrac{61}{11}}}{\dfrac{23}{5}-5-\dfrac{2}{3}-\left(-4+\dfrac{61}{11}\right)}}{\dfrac{2}{3}-5+\dfrac{61}{11}-9}\times\dfrac{86}{11}\\&=&\left(-9\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{86}{11}}{\dfrac{8}{7}}}{\dfrac{23}{5}-\dfrac{23}{5}+\dfrac{9874}{231}+\dfrac{61}{11}}}{\dfrac{23}{5}-5-\dfrac{2}{3}-\left(-4+\dfrac{61}{11}\right)}}{\dfrac{2}{3}-5+\dfrac{61}{11}-9}\times\dfrac{86}{11}\\&=&\left(-9\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{86}{11}}{\dfrac{8}{7}}}{\dfrac{23}{5}-\dfrac{23}{5}+\dfrac{9874}{231}+\dfrac{61}{11}}}{\dfrac{23}{5}-5-\dfrac{2}{3}-\dfrac{17}{11}}}{\dfrac{2}{3}-5+\dfrac{61}{11}-9}\times\dfrac{86}{11}\\&=&\left(-9\right)\times\dfrac{\dfrac{\dfrac{\dfrac{301}{44}}{\dfrac{23}{5}-\dfrac{23}{5}+\dfrac{9874}{231}+\dfrac{61}{11}}}{\dfrac{23}{5}-5-\dfrac{2}{3}-\dfrac{17}{11}}}{\dfrac{2}{3}-5+\dfrac{61}{11}-9}\times\dfrac{86}{11}\\&=&\left(-9\right)\times\dfrac{\dfrac{\dfrac{\dfrac{301}{44}}{0+\dfrac{9874}{231}+\dfrac{61}{11}}}{\dfrac{23}{5}-5-\dfrac{2}{3}-\dfrac{17}{11}}}{\dfrac{2}{3}-5+\dfrac{61}{11}-9}\times\dfrac{86}{11}\\&=&\left(-9\right)\times\dfrac{\dfrac{\dfrac{\dfrac{301}{44}}{\dfrac{9874}{231}+\dfrac{61}{11}}}{\dfrac{23}{5}-5-\dfrac{2}{3}-\dfrac{17}{11}}}{\dfrac{2}{3}-5+\dfrac{61}{11}-9}\times\dfrac{86}{11}\\&=&\left(-9\right)\times\dfrac{\dfrac{\dfrac{\dfrac{301}{44}}{\dfrac{11155}{231}}}{\dfrac{23}{5}-5-\dfrac{2}{3}-\dfrac{17}{11}}}{\dfrac{2}{3}-5+\dfrac{61}{11}-9}\times\dfrac{86}{11}\\&=&\left(-9\right)\times\dfrac{\dfrac{\dfrac{\dfrac{301}{44}}{\dfrac{11155}{231}}}{-\dfrac{2}{5}-\dfrac{2}{3}-\dfrac{17}{11}}}{\dfrac{2}{3}-5+\dfrac{61}{11}-9}\times\dfrac{86}{11}\\&=&\left(-9\right)\times\dfrac{\dfrac{\dfrac{\dfrac{301}{44}}{\dfrac{11155}{231}}}{-\dfrac{16}{15}-\dfrac{17}{11}}}{\dfrac{2}{3}-5+\dfrac{61}{11}-9}\times\dfrac{86}{11}\\&=&\left(-9\right)\times\dfrac{\dfrac{\dfrac{\dfrac{301}{44}}{\dfrac{11155}{231}}}{-\dfrac{431}{165}}}{\dfrac{2}{3}-5+\dfrac{61}{11}-9}\times\dfrac{86}{11}\\&=&\left(-9\right)\times\dfrac{\dfrac{\dfrac{\dfrac{301}{44}}{\dfrac{11155}{231}}}{-\dfrac{431}{165}}}{-\dfrac{13}{3}+\dfrac{61}{11}-9}\times\dfrac{86}{11}\\&=&\left(-9\right)\times\dfrac{\dfrac{\dfrac{\dfrac{301}{44}}{\dfrac{11155}{231}}}{-\dfrac{431}{165}}}{\dfrac{40}{33}-9}\times\dfrac{86}{11}\\&=&\left(-9\right)\times\dfrac{\dfrac{\dfrac{\dfrac{301}{44}}{\dfrac{11155}{231}}}{-\dfrac{431}{165}}}{-\dfrac{257}{33}}\times\dfrac{86}{11}\\&=&\left(-9\right)\times\dfrac{\dfrac{\dfrac{6321}{44620}}{-\dfrac{431}{165}}}{-\dfrac{257}{33}}\times\dfrac{86}{11}\\&=&\left(-9\right)\times\dfrac{-\dfrac{208593}{3846244}}{-\dfrac{257}{33}}\times\dfrac{86}{11}\\&=&\left(-9\right)\times\left(\dfrac{6883569}{988484708}\right)\times\dfrac{86}{11}\\&=&-\dfrac{61952121}{988484708}\times\dfrac{86}{11}\\&=&-\dfrac{5327882406}{10873331788}\\
\end{eqnarray*}