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 \[\dfrac{\dfrac{\dfrac{52}{7}+\dfrac{-\dfrac{23}{7}}{-7}-1+\dfrac{\dfrac{\left(-\dfrac{17}{8}\right)\times\left(-1\right)}{-\dfrac{73}{8}}}{-1}-\dfrac{73}{8}}{\dfrac{-\dfrac{73}{8}}{\dfrac{5+8}{-\dfrac{89}{10}-1}}}}{-\dfrac{89}{10}+\dfrac{4}{11}}-\dfrac{52}{7}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{\dfrac{\dfrac{52}{7}+\dfrac{-\dfrac{23}{7}}{-7}-1+\dfrac{\dfrac{\left(-\dfrac{17}{8}\right)\times\left(-1\right)}{-\dfrac{73}{8}}}{-1}-\dfrac{73}{8}}{\dfrac{-\dfrac{73}{8}}{\dfrac{5+8}{-\dfrac{89}{10}-1}}}}{-\dfrac{89}{10}+\dfrac{4}{11}}-\dfrac{52}{7}=-\dfrac{1256539396112}{169918484967}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{\dfrac{52}{7}+\dfrac{23}{49}-1+\dfrac{\dfrac{\left(-\dfrac{17}{8}\right)\times\left(-1\right)}{-\dfrac{73}{8}}}{-1}-\dfrac{73}{8}}{\dfrac{-\dfrac{73}{8}}{\dfrac{5+8}{-\dfrac{89}{10}-1}}}}{-\dfrac{89}{10}+\dfrac{4}{11}}-\dfrac{52}{7}\\&=&\dfrac{\dfrac{\dfrac{52}{7}+\dfrac{23}{49}-1+\dfrac{\dfrac{\dfrac{17}{8}}{-\dfrac{73}{8}}}{-1}-\dfrac{73}{8}}{\dfrac{-\dfrac{73}{8}}{\dfrac{5+8}{-\dfrac{89}{10}-1}}}}{-\dfrac{89}{10}+\dfrac{4}{11}}-\dfrac{52}{7}\\&=&\dfrac{\dfrac{\dfrac{52}{7}+\dfrac{23}{49}-1+\dfrac{\dfrac{\dfrac{17}{8}}{-\dfrac{73}{8}}}{-1}-\dfrac{73}{8}}{\dfrac{-\dfrac{73}{8}}{\dfrac{13}{-\dfrac{89}{10}-1}}}}{-\dfrac{89}{10}+\dfrac{4}{11}}-\dfrac{52}{7}\\&=&\dfrac{\dfrac{\dfrac{52}{7}+\dfrac{23}{49}-1+\dfrac{\dfrac{\dfrac{17}{8}}{-\dfrac{73}{8}}}{-1}-\dfrac{73}{8}}{\dfrac{-\dfrac{73}{8}}{\dfrac{13}{-\dfrac{99}{10}}}}}{-\dfrac{89}{10}+\dfrac{4}{11}}-\dfrac{52}{7}\\&=&\dfrac{\dfrac{\dfrac{387}{49}-1+\dfrac{\dfrac{\dfrac{17}{8}}{-\dfrac{73}{8}}}{-1}-\dfrac{73}{8}}{\dfrac{-\dfrac{73}{8}}{\dfrac{13}{-\dfrac{99}{10}}}}}{-\dfrac{89}{10}+\dfrac{4}{11}}-\dfrac{52}{7}\\&=&\dfrac{\dfrac{\dfrac{338}{49}+\dfrac{\dfrac{\dfrac{17}{8}}{-\dfrac{73}{8}}}{-1}-\dfrac{73}{8}}{\dfrac{-\dfrac{73}{8}}{\dfrac{13}{-\dfrac{99}{10}}}}}{-\dfrac{89}{10}+\dfrac{4}{11}}-\dfrac{52}{7}\\&=&\dfrac{\dfrac{\dfrac{338}{49}+\dfrac{-\dfrac{17}{73}}{-1}-\dfrac{73}{8}}{\dfrac{-\dfrac{73}{8}}{\dfrac{13}{-\dfrac{99}{10}}}}}{-\dfrac{89}{10}+\dfrac{4}{11}}-\dfrac{52}{7}\\&=&\dfrac{\dfrac{\dfrac{338}{49}+\dfrac{17}{73}-\dfrac{73}{8}}{\dfrac{-\dfrac{73}{8}}{\dfrac{13}{-\dfrac{99}{10}}}}}{-\dfrac{89}{10}+\dfrac{4}{11}}-\dfrac{52}{7}\\&=&\dfrac{\dfrac{\dfrac{338}{49}+\dfrac{17}{73}-\dfrac{73}{8}}{\dfrac{-\dfrac{73}{8}}{-\dfrac{130}{99}}}}{-\dfrac{89}{10}+\dfrac{4}{11}}-\dfrac{52}{7}\\&=&\dfrac{\dfrac{\dfrac{25507}{3577}-\dfrac{73}{8}}{\dfrac{-\dfrac{73}{8}}{-\dfrac{130}{99}}}}{-\dfrac{89}{10}+\dfrac{4}{11}}-\dfrac{52}{7}\\&=&\dfrac{\dfrac{-\dfrac{57065}{28616}}{\dfrac{-\dfrac{73}{8}}{-\dfrac{130}{99}}}}{-\dfrac{89}{10}+\dfrac{4}{11}}-\dfrac{52}{7}\\&=&\dfrac{\dfrac{-\dfrac{57065}{28616}}{\dfrac{7227}{1040}}}{-\dfrac{89}{10}+\dfrac{4}{11}}-\dfrac{52}{7}\\&=&\dfrac{\dfrac{-\dfrac{57065}{28616}}{\dfrac{7227}{1040}}}{-\dfrac{939}{110}}-\dfrac{52}{7}\\&=&\dfrac{-\dfrac{7418450}{25850979}}{-\dfrac{939}{110}}-\dfrac{52}{7}\\&=&\dfrac{816029500}{24274069281}-\dfrac{52}{7}\\&=&-\dfrac{1256539396112}{169918484967}\\
\end{eqnarray*}