L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\dfrac{6}{\dfrac{\dfrac{\left(10+3\right)\times\dfrac{-5}{7}\times\dfrac{1}{2}}{\left(7-\dfrac{60}{11}-6\right)-\left(10+\dfrac{1}{2}+10\right)}}{-\dfrac{94}{5}}}-\dfrac{94}{5}-\dfrac{31}{4}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{6}{\dfrac{\dfrac{\left(10+3\right)\times\dfrac{-5}{7}\times\dfrac{1}{2}}{\left(7-\dfrac{60}{11}-6\right)-\left(10+\dfrac{1}{2}+10\right)}}{-\dfrac{94}{5}}}-\dfrac{94}{5}-\dfrac{31}{4}=-\dfrac{9049473}{14300}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{6}{\dfrac{\dfrac{13\times\dfrac{-5}{7}\times\dfrac{1}{2}}{\left(7-\dfrac{60}{11}-6\right)-\left(10+\dfrac{1}{2}+10\right)}}{-\dfrac{94}{5}}}-\dfrac{94}{5}-\dfrac{31}{4}\\&=&\dfrac{6}{\dfrac{\dfrac{13\times\left(-\dfrac{5}{7}\right)\times\dfrac{1}{2}}{\left(7-\dfrac{60}{11}-6\right)-\left(10+\dfrac{1}{2}+10\right)}}{-\dfrac{94}{5}}}-\dfrac{94}{5}-\dfrac{31}{4}\\&=&\dfrac{6}{\dfrac{\dfrac{13\times\left(-\dfrac{5}{7}\right)\times\dfrac{1}{2}}{\left(\dfrac{17}{11}-6\right)-\left(10+\dfrac{1}{2}+10\right)}}{-\dfrac{94}{5}}}-\dfrac{94}{5}-\dfrac{31}{4}\\&=&\dfrac{6}{\dfrac{\dfrac{13\times\left(-\dfrac{5}{7}\right)\times\dfrac{1}{2}}{-\dfrac{49}{11}-\left(10+\dfrac{1}{2}+10\right)}}{-\dfrac{94}{5}}}-\dfrac{94}{5}-\dfrac{31}{4}\\&=&\dfrac{6}{\dfrac{\dfrac{13\times\left(-\dfrac{5}{7}\right)\times\dfrac{1}{2}}{-\dfrac{49}{11}-\left(\dfrac{21}{2}+10\right)}}{-\dfrac{94}{5}}}-\dfrac{94}{5}-\dfrac{31}{4}\\&=&\dfrac{6}{\dfrac{\dfrac{13\times\left(-\dfrac{5}{7}\right)\times\dfrac{1}{2}}{-\dfrac{49}{11}-\dfrac{41}{2}}}{-\dfrac{94}{5}}}-\dfrac{94}{5}-\dfrac{31}{4}\\&=&\dfrac{6}{\dfrac{\dfrac{\left(-\dfrac{65}{7}\right)\times\dfrac{1}{2}}{-\dfrac{49}{11}-\dfrac{41}{2}}}{-\dfrac{94}{5}}}-\dfrac{94}{5}-\dfrac{31}{4}\\&=&\dfrac{6}{\dfrac{\dfrac{-\dfrac{65}{14}}{-\dfrac{49}{11}-\dfrac{41}{2}}}{-\dfrac{94}{5}}}-\dfrac{94}{5}-\dfrac{31}{4}\\&=&\dfrac{6}{\dfrac{\dfrac{-\dfrac{65}{14}}{-\dfrac{549}{22}}}{-\dfrac{94}{5}}}-\dfrac{94}{5}-\dfrac{31}{4}\\&=&\dfrac{6}{\dfrac{\dfrac{715}{3843}}{-\dfrac{94}{5}}}-\dfrac{94}{5}-\dfrac{31}{4}\\&=&\dfrac{6}{-\dfrac{3575}{361242}}-\dfrac{94}{5}-\dfrac{31}{4}\\&=&-\dfrac{2167452}{3575}-\dfrac{94}{5}-\dfrac{31}{4}\\&=&-\dfrac{2234662}{3575}-\dfrac{31}{4}\\&=&-\dfrac{9049473}{14300}\\
\end{eqnarray*}