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Exercice

L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
Si vous regénérez la page (F5) les valeurs seront changées.
La correction se trouve en bas de page.

Exercice


Calculer \[\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\left(2+\dfrac{108}{5}+\left(-\dfrac{15}{7}\right)\times\left(-5\right)\right)-\dfrac{-8+4}{8-8-\dfrac{15}{7}-5}+5-\left(\dfrac{33}{7}-4-11-\left(-5-8+\dfrac{37}{8}-\dfrac{61}{7}\right)\right)}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\left(-\dfrac{15}{7}+9-6\right)\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times4\times\dfrac{\dfrac{\dfrac{\dfrac{61}{7}}{\dfrac{33}{7}}}{11}}{11}\times7\times8\times7+\dfrac{61}{7}\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\left(2+\dfrac{108}{5}+\left(-\dfrac{15}{7}\right)\times\left(-5\right)\right)-\dfrac{-8+4}{8-8-\dfrac{15}{7}-5}+5-\left(\dfrac{33}{7}-4-11-\left(-5-8+\dfrac{37}{8}-\dfrac{61}{7}\right)\right)}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\left(-\dfrac{15}{7}+9-6\right)\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times4\times\dfrac{\dfrac{\dfrac{\dfrac{61}{7}}{\dfrac{33}{7}}}{11}}{11}\times7\times8\times7+\dfrac{61}{7}=-\dfrac{1892960127390304}{551371795821}\) . Voici le détail : \begin{eqnarray*} X &=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\left(2+\dfrac{108}{5}+\dfrac{75}{7}\right)-\dfrac{-8+4}{8-8-\dfrac{15}{7}-5}+5-\left(\dfrac{33}{7}-4-11-\left(-5-8+\dfrac{37}{8}-\dfrac{61}{7}\right)\right)}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\left(-\dfrac{15}{7}+9-6\right)\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times4\times\dfrac{\dfrac{\dfrac{\dfrac{61}{7}}{\dfrac{33}{7}}}{11}}{11}\times7\times8\times7+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\left(2+\dfrac{108}{5}+\dfrac{75}{7}\right)-\dfrac{-4}{8-8-\dfrac{15}{7}-5}+5-\left(\dfrac{33}{7}-4-11-\left(-5-8+\dfrac{37}{8}-\dfrac{61}{7}\right)\right)}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\left(-\dfrac{15}{7}+9-6\right)\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times4\times\dfrac{\dfrac{\dfrac{\dfrac{61}{7}}{\dfrac{33}{7}}}{11}}{11}\times7\times8\times7+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\left(2+\dfrac{108}{5}+\dfrac{75}{7}\right)-\dfrac{-4}{0-\dfrac{15}{7}-5}+5-\left(\dfrac{33}{7}-4-11-\left(-5-8+\dfrac{37}{8}-\dfrac{61}{7}\right)\right)}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\left(-\dfrac{15}{7}+9-6\right)\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times4\times\dfrac{\dfrac{\dfrac{\dfrac{61}{7}}{\dfrac{33}{7}}}{11}}{11}\times7\times8\times7+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\left(2+\dfrac{108}{5}+\dfrac{75}{7}\right)-\dfrac{-4}{-\dfrac{15}{7}-5}+5-\left(\dfrac{33}{7}-4-11-\left(-5-8+\dfrac{37}{8}-\dfrac{61}{7}\right)\right)}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\left(-\dfrac{15}{7}+9-6\right)\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times4\times\dfrac{\dfrac{\dfrac{\dfrac{61}{7}}{\dfrac{33}{7}}}{11}}{11}\times7\times8\times7+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\left(2+\dfrac{108}{5}+\dfrac{75}{7}\right)-\dfrac{-4}{-\dfrac{50}{7}}+5-\left(\dfrac{33}{7}-4-11-\left(-5-8+\dfrac{37}{8}-\dfrac{61}{7}\right)\right)}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\left(-\dfrac{15}{7}+9-6\right)\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times4\times\dfrac{\dfrac{\dfrac{\dfrac{61}{7}}{\dfrac{33}{7}}}{11}}{11}\times7\times8\times7+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\left(2+\dfrac{108}{5}+\dfrac{75}{7}\right)-\dfrac{-4}{-\dfrac{50}{7}}+5-\left(\dfrac{33}{7}-4-11-\left(-13+\dfrac{37}{8}-\dfrac{61}{7}\right)\right)}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\left(-\dfrac{15}{7}+9-6\right)\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times4\times\dfrac{\dfrac{\dfrac{\dfrac{61}{7}}{\dfrac{33}{7}}}{11}}{11}\times7\times8\times7+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\left(2+\dfrac{108}{5}+\dfrac{75}{7}\right)-\dfrac{-4}{-\dfrac{50}{7}}+5-\left(\dfrac{33}{7}-4-11-\left(-\dfrac{67}{8}-\dfrac{61}{7}\right)\right)}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\left(-\dfrac{15}{7}+9-6\right)\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times4\times\dfrac{\dfrac{\dfrac{\dfrac{61}{7}}{\dfrac{33}{7}}}{11}}{11}\times7\times8\times7+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\left(2+\dfrac{108}{5}+\dfrac{75}{7}\right)-\dfrac{-4}{-\dfrac{50}{7}}+5-\left(\dfrac{33}{7}-4-11+\dfrac{957}{56}\right)}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\left(-\dfrac{15}{7}+9-6\right)\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times4\times\dfrac{\dfrac{\dfrac{\dfrac{61}{7}}{\dfrac{33}{7}}}{11}}{11}\times7\times8\times7+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\left(2+\dfrac{108}{5}+\dfrac{75}{7}\right)-\dfrac{-4}{-\dfrac{50}{7}}+5-\left(\dfrac{33}{7}-4-11+\dfrac{957}{56}\right)}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\left(-\dfrac{15}{7}+9-6\right)\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times4\times\dfrac{\dfrac{\dfrac{61}{33}}{11}}{11}\times7\times8\times7+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\left(2+\dfrac{108}{5}+\dfrac{75}{7}\right)-\dfrac{-4}{-\dfrac{50}{7}}+5-\left(\dfrac{33}{7}-4-11+\dfrac{957}{56}\right)}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\left(-\dfrac{15}{7}+9-6\right)\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times4\times\dfrac{\dfrac{61}{363}}{11}\times7\times8\times7+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\left(2+\dfrac{108}{5}+\dfrac{75}{7}\right)-\dfrac{-4}{-\dfrac{50}{7}}+5-\left(\dfrac{33}{7}-4-11+\dfrac{957}{56}\right)}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\left(-\dfrac{15}{7}+9-6\right)\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times4\times\dfrac{61}{3993}\times7\times8\times7+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\left(2+\dfrac{108}{5}+\dfrac{75}{7}\right)-\dfrac{-4}{-\dfrac{50}{7}}+5-\left(\dfrac{33}{7}-4-11+\dfrac{957}{56}\right)}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\left(-\dfrac{15}{7}+9-6\right)\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times4\times\dfrac{61}{3993}\times56\times7+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\left(2+\dfrac{108}{5}+\dfrac{75}{7}\right)-\dfrac{-4}{-\dfrac{50}{7}}+5-\left(\dfrac{33}{7}-4-11+\dfrac{957}{56}\right)}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\left(-\dfrac{15}{7}+9-6\right)\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times4\times\dfrac{61}{3993}\times392+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\left(\dfrac{118}{5}+\dfrac{75}{7}\right)-\dfrac{-4}{-\dfrac{50}{7}}+5-\left(\dfrac{33}{7}-4-11+\dfrac{957}{56}\right)}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\left(-\dfrac{15}{7}+9-6\right)\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times4\times\dfrac{61}{3993}\times392+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\dfrac{1201}{35}-\dfrac{-4}{-\dfrac{50}{7}}+5-\left(\dfrac{33}{7}-4-11+\dfrac{957}{56}\right)}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\left(-\dfrac{15}{7}+9-6\right)\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times4\times\dfrac{61}{3993}\times392+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\dfrac{1201}{35}-\dfrac{14}{25}+5-\left(\dfrac{33}{7}-4-11+\dfrac{957}{56}\right)}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\left(-\dfrac{15}{7}+9-6\right)\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times4\times\dfrac{61}{3993}\times392+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\dfrac{1201}{35}-\dfrac{14}{25}+5-\left(\dfrac{5}{7}-11+\dfrac{957}{56}\right)}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\left(-\dfrac{15}{7}+9-6\right)\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times4\times\dfrac{61}{3993}\times392+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\dfrac{1201}{35}-\dfrac{14}{25}+5-\left(-\dfrac{72}{7}+\dfrac{957}{56}\right)}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\left(-\dfrac{15}{7}+9-6\right)\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times4\times\dfrac{61}{3993}\times392+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\dfrac{1201}{35}-\dfrac{14}{25}+5-\dfrac{381}{56}}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\left(-\dfrac{15}{7}+9-6\right)\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times4\times\dfrac{61}{3993}\times392+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\dfrac{1201}{35}-\dfrac{14}{25}+5-\dfrac{381}{56}}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\left(\dfrac{48}{7}-6\right)\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times4\times\dfrac{61}{3993}\times392+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\dfrac{1201}{35}-\dfrac{14}{25}+5-\dfrac{381}{56}}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\dfrac{6}{7}\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times4\times\dfrac{61}{3993}\times392+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\dfrac{1201}{35}-\dfrac{14}{25}+5-\dfrac{381}{56}}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\dfrac{6}{7}\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times\dfrac{244}{3993}\times392+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\dfrac{1201}{35}-\dfrac{14}{25}+5-\dfrac{381}{56}}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\dfrac{6}{7}\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times\dfrac{95648}{3993}+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\dfrac{5907}{175}+5-\dfrac{381}{56}}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\dfrac{6}{7}\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times\dfrac{95648}{3993}+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\dfrac{6782}{175}-\dfrac{381}{56}}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\dfrac{6}{7}\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times\dfrac{95648}{3993}+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\dfrac{44731}{1400}}+\dfrac{61}{7}+\left(-8+7\right)\times\dfrac{61}{7}\times\dfrac{6}{7}\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times\dfrac{95648}{3993}+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\dfrac{44731}{1400}}+\dfrac{61}{7}-1\times\dfrac{61}{7}\times\dfrac{6}{7}\times\left(-9\right)\times\left(-\dfrac{15}{7}\right)\times\dfrac{95648}{3993}+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\dfrac{44731}{1400}}+\dfrac{61}{7}-1\times\dfrac{61}{7}\times\left(-\dfrac{54}{7}\right)\times\left(-\dfrac{15}{7}\right)\times\dfrac{95648}{3993}+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\dfrac{44731}{1400}}+\dfrac{61}{7}-1\times\dfrac{61}{7}\times\dfrac{810}{49}\times\dfrac{95648}{3993}+\dfrac{61}{7}\\&=&\dfrac{\dfrac{7}{\dfrac{108}{5}}}{\dfrac{44731}{1400}}+\dfrac{61}{7}-1\times\dfrac{61}{7}\times\dfrac{527040}{1331}+\dfrac{61}{7}\\&=&\dfrac{\dfrac{35}{108}}{\dfrac{44731}{1400}}+\dfrac{61}{7}-1\times\dfrac{61}{7}\times\dfrac{527040}{1331}+\dfrac{61}{7}\\&=&\dfrac{12250}{1207737}+\dfrac{61}{7}-1\times\dfrac{61}{7}\times\dfrac{527040}{1331}+\dfrac{61}{7}\\&=&\dfrac{12250}{1207737}+\dfrac{61}{7}-\dfrac{61}{7}\times\dfrac{527040}{1331}+\dfrac{61}{7}\\&=&\dfrac{12250}{1207737}+\dfrac{61}{7}-\dfrac{32149440}{9317}+\dfrac{61}{7}\\&=&\dfrac{73757707}{8454159}-\dfrac{32149440}{9317}+\dfrac{61}{7}\\&=&-\dfrac{271109276964841}{78767399403}+\dfrac{61}{7}\\&=&-\dfrac{1892960127390304}{551371795821}\\ \end{eqnarray*}