L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[-\dfrac{96}{5}+\dfrac{-\dfrac{32}{3}}{\dfrac{\dfrac{10\times7\times\dfrac{13}{4}}{-\dfrac{96}{5}}}{-11+\dfrac{57}{2}-7}\times\dfrac{57}{2}}+\dfrac{-\dfrac{96}{5}}{-\dfrac{96}{5}+7-\left(\dfrac{\dfrac{-3}{8}}{\dfrac{57}{2}}-12+3\right)}\]
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Exercice
On a \( X=-\dfrac{96}{5}+\dfrac{-\dfrac{32}{3}}{\dfrac{\dfrac{10\times7\times\dfrac{13}{4}}{-\dfrac{96}{5}}}{-11+\dfrac{57}{2}-7}\times\dfrac{57}{2}}+\dfrac{-\dfrac{96}{5}}{-\dfrac{96}{5}+7-\left(\dfrac{\dfrac{-3}{8}}{\dfrac{57}{2}}-12+3\right)}=-\dfrac{96043232}{7477925}\) . Voici le détail :
\begin{eqnarray*}
X &=&-\dfrac{96}{5}+\dfrac{-\dfrac{32}{3}}{\dfrac{\dfrac{70\times\dfrac{13}{4}}{-\dfrac{96}{5}}}{-11+\dfrac{57}{2}-7}\times\dfrac{57}{2}}+\dfrac{-\dfrac{96}{5}}{-\dfrac{96}{5}+7-\left(\dfrac{\dfrac{-3}{8}}{\dfrac{57}{2}}-12+3\right)}\\&=&-\dfrac{96}{5}+\dfrac{-\dfrac{32}{3}}{\dfrac{\dfrac{\dfrac{455}{2}}{-\dfrac{96}{5}}}{-11+\dfrac{57}{2}-7}\times\dfrac{57}{2}}+\dfrac{-\dfrac{96}{5}}{-\dfrac{96}{5}+7-\left(\dfrac{\dfrac{-3}{8}}{\dfrac{57}{2}}-12+3\right)}\\&=&-\dfrac{96}{5}+\dfrac{-\dfrac{32}{3}}{\dfrac{\dfrac{\dfrac{455}{2}}{-\dfrac{96}{5}}}{\dfrac{35}{2}-7}\times\dfrac{57}{2}}+\dfrac{-\dfrac{96}{5}}{-\dfrac{96}{5}+7-\left(\dfrac{\dfrac{-3}{8}}{\dfrac{57}{2}}-12+3\right)}\\&=&-\dfrac{96}{5}+\dfrac{-\dfrac{32}{3}}{\dfrac{\dfrac{\dfrac{455}{2}}{-\dfrac{96}{5}}}{\dfrac{21}{2}}\times\dfrac{57}{2}}+\dfrac{-\dfrac{96}{5}}{-\dfrac{96}{5}+7-\left(\dfrac{\dfrac{-3}{8}}{\dfrac{57}{2}}-12+3\right)}\\&=&-\dfrac{96}{5}+\dfrac{-\dfrac{32}{3}}{\dfrac{\dfrac{\dfrac{455}{2}}{-\dfrac{96}{5}}}{\dfrac{21}{2}}\times\dfrac{57}{2}}+\dfrac{-\dfrac{96}{5}}{-\dfrac{96}{5}+7-\left(\dfrac{-\dfrac{3}{8}}{\dfrac{57}{2}}-12+3\right)}\\&=&-\dfrac{96}{5}+\dfrac{-\dfrac{32}{3}}{\dfrac{\dfrac{\dfrac{455}{2}}{-\dfrac{96}{5}}}{\dfrac{21}{2}}\times\dfrac{57}{2}}+\dfrac{-\dfrac{96}{5}}{-\dfrac{96}{5}+7-\left(-\dfrac{1}{76}-12+3\right)}\\&=&-\dfrac{96}{5}+\dfrac{-\dfrac{32}{3}}{\dfrac{-\dfrac{2275}{192}}{\dfrac{21}{2}}\times\dfrac{57}{2}}+\dfrac{-\dfrac{96}{5}}{-\dfrac{96}{5}+7-\left(-\dfrac{1}{76}-12+3\right)}\\&=&-\dfrac{96}{5}+\dfrac{-\dfrac{32}{3}}{\left(-\dfrac{325}{288}\right)\times\dfrac{57}{2}}+\dfrac{-\dfrac{96}{5}}{-\dfrac{96}{5}+7-\left(-\dfrac{1}{76}-12+3\right)}\\&=&-\dfrac{96}{5}+\dfrac{-\dfrac{32}{3}}{\left(-\dfrac{325}{288}\right)\times\dfrac{57}{2}}+\dfrac{-\dfrac{96}{5}}{-\dfrac{96}{5}+7-\left(-\dfrac{913}{76}+3\right)}\\&=&-\dfrac{96}{5}+\dfrac{-\dfrac{32}{3}}{\left(-\dfrac{325}{288}\right)\times\dfrac{57}{2}}+\dfrac{-\dfrac{96}{5}}{-\dfrac{96}{5}+7+\dfrac{685}{76}}\\&=&-\dfrac{96}{5}+\dfrac{-\dfrac{32}{3}}{-\dfrac{6175}{192}}+\dfrac{-\dfrac{96}{5}}{-\dfrac{96}{5}+7+\dfrac{685}{76}}\\&=&-\dfrac{96}{5}+\dfrac{-\dfrac{32}{3}}{-\dfrac{6175}{192}}+\dfrac{-\dfrac{96}{5}}{-\dfrac{61}{5}+\dfrac{685}{76}}\\&=&-\dfrac{96}{5}+\dfrac{-\dfrac{32}{3}}{-\dfrac{6175}{192}}+\dfrac{-\dfrac{96}{5}}{-\dfrac{1211}{380}}\\&=&-\dfrac{96}{5}+\dfrac{2048}{6175}+\dfrac{-\dfrac{96}{5}}{-\dfrac{1211}{380}}\\&=&-\dfrac{96}{5}+\dfrac{2048}{6175}+\dfrac{7296}{1211}\\&=&-\dfrac{116512}{6175}+\dfrac{7296}{1211}\\&=&-\dfrac{96043232}{7477925}\\
\end{eqnarray*}