L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\left(-6+\left(-\dfrac{3}{8}\right)\times\dfrac{\dfrac{55}{3}}{\dfrac{39}{2}}\times6\times\dfrac{55}{3}-\dfrac{52}{5}+4\right)-4-\dfrac{-\dfrac{52}{5}-\dfrac{4\times\dfrac{55}{2}\times\dfrac{55}{3}\times\dfrac{121}{12}}{\dfrac{142}{9}}-8}{\dfrac{68}{3}\times\left(-4\right)}+\dfrac{20}{3}\]
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Exercice
On a \( X=\left(-6+\left(-\dfrac{3}{8}\right)\times\dfrac{\dfrac{55}{3}}{\dfrac{39}{2}}\times6\times\dfrac{55}{3}-\dfrac{52}{5}+4\right)-4-\dfrac{-\dfrac{52}{5}-\dfrac{4\times\dfrac{55}{2}\times\dfrac{55}{3}\times\dfrac{121}{12}}{\dfrac{142}{9}}-8}{\dfrac{68}{3}\times\left(-4\right)}+\dfrac{20}{3}=-\dfrac{28439589150}{451900800}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(-6+\left(-\dfrac{3}{8}\right)\times\dfrac{\dfrac{55}{3}}{\dfrac{39}{2}}\times6\times\dfrac{55}{3}-\dfrac{52}{5}+4\right)-4-\dfrac{-\dfrac{52}{5}-\dfrac{110\times\dfrac{55}{3}\times\dfrac{121}{12}}{\dfrac{142}{9}}-8}{\dfrac{68}{3}\times\left(-4\right)}+\dfrac{20}{3}\\&=&\left(-6+\left(-\dfrac{3}{8}\right)\times\dfrac{\dfrac{55}{3}}{\dfrac{39}{2}}\times6\times\dfrac{55}{3}-\dfrac{52}{5}+4\right)-4-\dfrac{-\dfrac{52}{5}-\dfrac{\dfrac{6050}{3}\times\dfrac{121}{12}}{\dfrac{142}{9}}-8}{\dfrac{68}{3}\times\left(-4\right)}+\dfrac{20}{3}\\&=&\left(-6+\left(-\dfrac{3}{8}\right)\times\dfrac{\dfrac{55}{3}}{\dfrac{39}{2}}\times6\times\dfrac{55}{3}-\dfrac{52}{5}+4\right)-4-\dfrac{-\dfrac{52}{5}-\dfrac{\dfrac{366025}{18}}{\dfrac{142}{9}}-8}{\dfrac{68}{3}\times\left(-4\right)}+\dfrac{20}{3}\\&=&\left(-6+\left(-\dfrac{3}{8}\right)\times\dfrac{110}{117}\times6\times\dfrac{55}{3}-\dfrac{52}{5}+4\right)-4-\dfrac{-\dfrac{52}{5}-\dfrac{\dfrac{366025}{18}}{\dfrac{142}{9}}-8}{\dfrac{68}{3}\times\left(-4\right)}+\dfrac{20}{3}\\&=&\left(-6+\left(-\dfrac{3}{8}\right)\times\dfrac{110}{117}\times6\times\dfrac{55}{3}-\dfrac{52}{5}+4\right)-4-\dfrac{-\dfrac{52}{5}-\dfrac{366025}{284}-8}{\dfrac{68}{3}\times\left(-4\right)}+\dfrac{20}{3}\\&=&\left(-6+\left(-\dfrac{55}{156}\right)\times6\times\dfrac{55}{3}-\dfrac{52}{5}+4\right)-4-\dfrac{-\dfrac{52}{5}-\dfrac{366025}{284}-8}{\dfrac{68}{3}\times\left(-4\right)}+\dfrac{20}{3}\\&=&\left(-6+\left(-\dfrac{55}{26}\right)\times\dfrac{55}{3}-\dfrac{52}{5}+4\right)-4-\dfrac{-\dfrac{52}{5}-\dfrac{366025}{284}-8}{\dfrac{68}{3}\times\left(-4\right)}+\dfrac{20}{3}\\&=&\left(-6-\dfrac{3025}{78}-\dfrac{52}{5}+4\right)-4-\dfrac{-\dfrac{52}{5}-\dfrac{366025}{284}-8}{\dfrac{68}{3}\times\left(-4\right)}+\dfrac{20}{3}\\&=&\left(-6-\dfrac{3025}{78}-\dfrac{52}{5}+4\right)-4-\dfrac{-\dfrac{1844893}{1420}-8}{\dfrac{68}{3}\times\left(-4\right)}+\dfrac{20}{3}\\&=&\left(-6-\dfrac{3025}{78}-\dfrac{52}{5}+4\right)-4-\dfrac{-\dfrac{1856253}{1420}}{\dfrac{68}{3}\times\left(-4\right)}+\dfrac{20}{3}\\&=&\left(-6-\dfrac{3025}{78}-\dfrac{52}{5}+4\right)-4-\dfrac{-\dfrac{1856253}{1420}}{-\dfrac{272}{3}}+\dfrac{20}{3}\\&=&\left(-\dfrac{3493}{78}-\dfrac{52}{5}+4\right)-4-\dfrac{-\dfrac{1856253}{1420}}{-\dfrac{272}{3}}+\dfrac{20}{3}\\&=&\left(-\dfrac{21521}{390}+4\right)-4-\dfrac{-\dfrac{1856253}{1420}}{-\dfrac{272}{3}}+\dfrac{20}{3}\\&=&-\dfrac{19961}{390}-4-\dfrac{-\dfrac{1856253}{1420}}{-\dfrac{272}{3}}+\dfrac{20}{3}\\&=&-\dfrac{19961}{390}-4-\dfrac{5568759}{386240}+\dfrac{20}{3}\\&=&-\dfrac{21521}{390}-\dfrac{5568759}{386240}+\dfrac{20}{3}\\&=&-\dfrac{10484087050}{150633600}+\dfrac{20}{3}\\&=&-\dfrac{28439589150}{451900800}\\
\end{eqnarray*}