Ataraxy

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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 \[\dfrac{\left(\left(-2+\dfrac{29}{2}+\dfrac{\dfrac{-\dfrac{26}{3}}{-\dfrac{67}{10}}}{-4}-4\right)-\dfrac{65}{9}\right)-\left(\dfrac{29}{2}+\dfrac{140}{11}-2+\dfrac{29}{2}\right)-\left(\dfrac{140}{11}-4-\left(12+4+12+\dfrac{41}{2}\right)+\dfrac{73}{8}+\dfrac{-\dfrac{26}{3}}{12}\right)}{\dfrac{73}{8}\times\left(-4\right)\times\left(-\dfrac{26}{3}\right)\times\left(-4\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-4}{4}}{\dfrac{140}{11}}}{-\dfrac{67}{10}}}{-2}}{-4}}\]

Cliquer ici pour afficher la solution

Exercice

On a $ X=\dfrac{\left(\left(-2+\dfrac{29}{2}+\dfrac{\dfrac{-\dfrac{26}{3}}{-\dfrac{67}{10}}}{-4}-4\right)-\dfrac{65}{9}\right)-\left(\dfrac{29}{2}+\dfrac{140}{11}-2+\dfrac{29}{2}\right)-\left(\dfrac{140}{11}-4-\left(12+4+12+\dfrac{41}{2}\right)+\dfrac{73}{8}+\dfrac{-\dfrac{26}{3}}{12}\right)}{\dfrac{73}{8}\times\left(-4\right)\times\left(-\dfrac{26}{3}\right)\times\left(-4\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-4}{4}}{\dfrac{140}{11}}}{-\dfrac{67}{10}}}{-2}}{-4}}=\dfrac{916601}{229658}$ . Voici le détail : \begin{eqnarray*} X &=&\dfrac{\left(\left(-2+\dfrac{29}{2}+\dfrac{\dfrac{260}{201}}{-4}-4\right)-\dfrac{65}{9}\right)-\left(\dfrac{29}{2}+\dfrac{140}{11}-2+\dfrac{29}{2}\right)-\left(\dfrac{140}{11}-4-\left(12+4+12+\dfrac{41}{2}\right)+\dfrac{73}{8}+\dfrac{-\dfrac{26}{3}}{12}\right)}{\dfrac{73}{8}\times\left(-4\right)\times\left(-\dfrac{26}{3}\right)\times\left(-4\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-4}{4}}{\dfrac{140}{11}}}{-\dfrac{67}{10}}}{-2}}{-4}}\\&=&\dfrac{\left(\left(-2+\dfrac{29}{2}-\dfrac{65}{201}-4\right)-\dfrac{65}{9}\right)-\left(\dfrac{29}{2}+\dfrac{140}{11}-2+\dfrac{29}{2}\right)-\left(\dfrac{140}{11}-4-\left(12+4+12+\dfrac{41}{2}\right)+\dfrac{73}{8}+\dfrac{-\dfrac{26}{3}}{12}\right)}{\dfrac{73}{8}\times\left(-4\right)\times\left(-\dfrac{26}{3}\right)\times\left(-4\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-4}{4}}{\dfrac{140}{11}}}{-\dfrac{67}{10}}}{-2}}{-4}}\\&=&\dfrac{\left(\left(-2+\dfrac{29}{2}-\dfrac{65}{201}-4\right)-\dfrac{65}{9}\right)-\left(\dfrac{29}{2}+\dfrac{140}{11}-2+\dfrac{29}{2}\right)-\left(\dfrac{140}{11}-4-\left(16+12+\dfrac{41}{2}\right)+\dfrac{73}{8}+\dfrac{-\dfrac{26}{3}}{12}\right)}{\dfrac{73}{8}\times\left(-4\right)\times\left(-\dfrac{26}{3}\right)\times\left(-4\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-4}{4}}{\dfrac{140}{11}}}{-\dfrac{67}{10}}}{-2}}{-4}}\\&=&\dfrac{\left(\left(-2+\dfrac{29}{2}-\dfrac{65}{201}-4\right)-\dfrac{65}{9}\right)-\left(\dfrac{29}{2}+\dfrac{140}{11}-2+\dfrac{29}{2}\right)-\left(\dfrac{140}{11}-4-\left(28+\dfrac{41}{2}\right)+\dfrac{73}{8}+\dfrac{-\dfrac{26}{3}}{12}\right)}{\dfrac{73}{8}\times\left(-4\right)\times\left(-\dfrac{26}{3}\right)\times\left(-4\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-4}{4}}{\dfrac{140}{11}}}{-\dfrac{67}{10}}}{-2}}{-4}}\\&=&\dfrac{\left(\left(-2+\dfrac{29}{2}-\dfrac{65}{201}-4\right)-\dfrac{65}{9}\right)-\left(\dfrac{29}{2}+\dfrac{140}{11}-2+\dfrac{29}{2}\right)-\left(\dfrac{140}{11}-4-\dfrac{97}{2}+\dfrac{73}{8}+\dfrac{-\dfrac{26}{3}}{12}\right)}{\dfrac{73}{8}\times\left(-4\right)\times\left(-\dfrac{26}{3}\right)\times\left(-4\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-4}{4}}{\dfrac{140}{11}}}{-\dfrac{67}{10}}}{-2}}{-4}}\\&=&\dfrac{\left(\left(\dfrac{25}{2}-\dfrac{65}{201}-4\right)-\dfrac{65}{9}\right)-\left(\dfrac{29}{2}+\dfrac{140}{11}-2+\dfrac{29}{2}\right)-\left(\dfrac{140}{11}-4-\dfrac{97}{2}+\dfrac{73}{8}+\dfrac{-\dfrac{26}{3}}{12}\right)}{\dfrac{73}{8}\times\left(-4\right)\times\left(-\dfrac{26}{3}\right)\times\left(-4\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-4}{4}}{\dfrac{140}{11}}}{-\dfrac{67}{10}}}{-2}}{-4}}\\&=&\dfrac{\left(\left(\dfrac{4895}{402}-4\right)-\dfrac{65}{9}\right)-\left(\dfrac{29}{2}+\dfrac{140}{11}-2+\dfrac{29}{2}\right)-\left(\dfrac{140}{11}-4-\dfrac{97}{2}+\dfrac{73}{8}+\dfrac{-\dfrac{26}{3}}{12}\right)}{\dfrac{73}{8}\times\left(-4\right)\times\left(-\dfrac{26}{3}\right)\times\left(-4\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-4}{4}}{\dfrac{140}{11}}}{-\dfrac{67}{10}}}{-2}}{-4}}\\&=&\dfrac{\left(\dfrac{3287}{402}-\dfrac{65}{9}\right)-\left(\dfrac{29}{2}+\dfrac{140}{11}-2+\dfrac{29}{2}\right)-\left(\dfrac{140}{11}-4-\dfrac{97}{2}+\dfrac{73}{8}+\dfrac{-\dfrac{26}{3}}{12}\right)}{\dfrac{73}{8}\times\left(-4\right)\times\left(-\dfrac{26}{3}\right)\times\left(-4\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-4}{4}}{\dfrac{140}{11}}}{-\dfrac{67}{10}}}{-2}}{-4}}\\&=&\dfrac{\left(\dfrac{3287}{402}-\dfrac{65}{9}\right)-\left(\dfrac{29}{2}+\dfrac{140}{11}-2+\dfrac{29}{2}\right)-\left(\dfrac{96}{11}-\dfrac{97}{2}+\dfrac{73}{8}+\dfrac{-\dfrac{26}{3}}{12}\right)}{\dfrac{73}{8}\times\left(-4\right)\times\left(-\dfrac{26}{3}\right)\times\left(-4\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-4}{4}}{\dfrac{140}{11}}}{-\dfrac{67}{10}}}{-2}}{-4}}\\&=&\dfrac{\left(\dfrac{3287}{402}-\dfrac{65}{9}\right)-\left(\dfrac{29}{2}+\dfrac{140}{11}-2+\dfrac{29}{2}\right)-\left(-\dfrac{875}{22}+\dfrac{73}{8}+\dfrac{-\dfrac{26}{3}}{12}\right)}{\dfrac{73}{8}\times\left(-4\right)\times\left(-\dfrac{26}{3}\right)\times\left(-4\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-4}{4}}{\dfrac{140}{11}}}{-\dfrac{67}{10}}}{-2}}{-4}}\\&=&\dfrac{\left(\dfrac{3287}{402}-\dfrac{65}{9}\right)-\left(\dfrac{29}{2}+\dfrac{140}{11}-2+\dfrac{29}{2}\right)-\left(-\dfrac{875}{22}+\dfrac{73}{8}-\dfrac{13}{18}\right)}{\dfrac{73}{8}\times\left(-4\right)\times\left(-\dfrac{26}{3}\right)\times\left(-4\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-4}{4}}{\dfrac{140}{11}}}{-\dfrac{67}{10}}}{-2}}{-4}}\\&=&\dfrac{\left(\dfrac{3287}{402}-\dfrac{65}{9}\right)-\left(\dfrac{29}{2}+\dfrac{140}{11}-2+\dfrac{29}{2}\right)-\left(-\dfrac{875}{22}+\dfrac{73}{8}-\dfrac{13}{18}\right)}{\dfrac{73}{8}\times\left(-4\right)\times\left(-\dfrac{26}{3}\right)\times\left(-4\right)\times\dfrac{\dfrac{\dfrac{\dfrac{-1}{\dfrac{140}{11}}}{-\dfrac{67}{10}}}{-2}}{-4}}\\&=&\dfrac{\left(\dfrac{3287}{402}-\dfrac{65}{9}\right)-\left(\dfrac{29}{2}+\dfrac{140}{11}-2+\dfrac{29}{2}\right)-\left(-\dfrac{875}{22}+\dfrac{73}{8}-\dfrac{13}{18}\right)}{\dfrac{73}{8}\times\left(-4\right)\times\left(-\dfrac{26}{3}\right)\times\left(-4\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{11}{140}}{-\dfrac{67}{10}}}{-2}}{-4}}\\&=&\dfrac{\dfrac{1151}{1206}-\left(\dfrac{29}{2}+\dfrac{140}{11}-2+\dfrac{29}{2}\right)-\left(-\dfrac{875}{22}+\dfrac{73}{8}-\dfrac{13}{18}\right)}{\dfrac{73}{8}\times\left(-4\right)\times\left(-\dfrac{26}{3}\right)\times\left(-4\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{11}{140}}{-\dfrac{67}{10}}}{-2}}{-4}}\\&=&\dfrac{\dfrac{1151}{1206}-\left(\dfrac{599}{22}-2+\dfrac{29}{2}\right)-\left(-\dfrac{875}{22}+\dfrac{73}{8}-\dfrac{13}{18}\right)}{\dfrac{73}{8}\times\left(-4\right)\times\left(-\dfrac{26}{3}\right)\times\left(-4\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{11}{140}}{-\dfrac{67}{10}}}{-2}}{-4}}\\&=&\dfrac{\dfrac{1151}{1206}-\left(\dfrac{555}{22}+\dfrac{29}{2}\right)-\left(-\dfrac{875}{22}+\dfrac{73}{8}-\dfrac{13}{18}\right)}{\dfrac{73}{8}\times\left(-4\right)\times\left(-\dfrac{26}{3}\right)\times\left(-4\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{11}{140}}{-\dfrac{67}{10}}}{-2}}{-4}}\\&=&\dfrac{\dfrac{1151}{1206}-\dfrac{437}{11}-\left(-\dfrac{875}{22}+\dfrac{73}{8}-\dfrac{13}{18}\right)}{\dfrac{73}{8}\times\left(-4\right)\times\left(-\dfrac{26}{3}\right)\times\left(-4\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{11}{140}}{-\dfrac{67}{10}}}{-2}}{-4}}\\&=&\dfrac{\dfrac{1151}{1206}-\dfrac{437}{11}-\left(-\dfrac{2697}{88}-\dfrac{13}{18}\right)}{\dfrac{73}{8}\times\left(-4\right)\times\left(-\dfrac{26}{3}\right)\times\left(-4\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{11}{140}}{-\dfrac{67}{10}}}{-2}}{-4}}\\&=&\dfrac{\dfrac{1151}{1206}-\dfrac{437}{11}+\dfrac{24845}{792}}{\dfrac{73}{8}\times\left(-4\right)\times\left(-\dfrac{26}{3}\right)\times\left(-4\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{11}{140}}{-\dfrac{67}{10}}}{-2}}{-4}}\\&=&\dfrac{\dfrac{1151}{1206}-\dfrac{437}{11}+\dfrac{24845}{792}}{\left(-\dfrac{73}{2}\right)\times\left(-\dfrac{26}{3}\right)\times\left(-4\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{11}{140}}{-\dfrac{67}{10}}}{-2}}{-4}}\\&=&\dfrac{\dfrac{1151}{1206}-\dfrac{437}{11}+\dfrac{24845}{792}}{\dfrac{949}{3}\times\left(-4\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{11}{140}}{-\dfrac{67}{10}}}{-2}}{-4}}\\&=&\dfrac{\dfrac{1151}{1206}-\dfrac{437}{11}+\dfrac{24845}{792}}{\left(-\dfrac{3796}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{11}{140}}{-\dfrac{67}{10}}}{-2}}{-4}}\\&=&\dfrac{\dfrac{1151}{1206}-\dfrac{437}{11}+\dfrac{24845}{792}}{\left(-\dfrac{3796}{3}\right)\times\dfrac{\dfrac{\dfrac{11}{938}}{-2}}{-4}}\\&=&\dfrac{\dfrac{1151}{1206}-\dfrac{437}{11}+\dfrac{24845}{792}}{\left(-\dfrac{3796}{3}\right)\times\dfrac{-\dfrac{11}{1876}}{-4}}\\&=&\dfrac{\dfrac{1151}{1206}-\dfrac{437}{11}+\dfrac{24845}{792}}{\left(-\dfrac{3796}{3}\right)\times\dfrac{11}{7504}}\\&=&\dfrac{-\dfrac{514361}{13266}+\dfrac{24845}{792}}{\left(-\dfrac{3796}{3}\right)\times\dfrac{11}{7504}}\\&=&\dfrac{-\dfrac{130943}{17688}}{\left(-\dfrac{3796}{3}\right)\times\dfrac{11}{7504}}\\&=&\dfrac{-\dfrac{130943}{17688}}{-\dfrac{10439}{5628}}\\&=&\dfrac{916601}{229658}\\ \end{eqnarray*}