L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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Exercice
Calculer \[-\dfrac{58}{17}-\dfrac{15}{-19}-19+13+\dfrac{-13+\left(-13\right)\times\left(-\dfrac{28}{3}+\dfrac{28}{3}+\dfrac{167}{18}\right)+\left(-13\right)\times\dfrac{253}{6}\times\left(-\dfrac{167}{18}+\dfrac{91}{2}-\dfrac{315}{13}\right)\times\left(-\dfrac{167}{18}\right)\times\left(-19\right)\times\left(-\dfrac{167}{18}\right)\times\left(-19\right)}{-\dfrac{58}{17}}\times\left(-15-\dfrac{253}{6}\right)\times\left(-\dfrac{69}{17}\right)\times\left(-\dfrac{190}{3}\right)\times\dfrac{253}{6}\times\dfrac{-2}{-\dfrac{28}{3}+\dfrac{253}{6}}\times\left(-15\right)\times\left(-\dfrac{28}{3}\right)\times\left(-\dfrac{91}{2}\right)\times\dfrac{253}{6}\]
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Exercice
On a \( X=-\dfrac{58}{17}-\dfrac{15}{-19}-19+13+\dfrac{-13+\left(-13\right)\times\left(-\dfrac{28}{3}+\dfrac{28}{3}+\dfrac{167}{18}\right)+\left(-13\right)\times\dfrac{253}{6}\times\left(-\dfrac{167}{18}+\dfrac{91}{2}-\dfrac{315}{13}\right)\times\left(-\dfrac{167}{18}\right)\times\left(-19\right)\times\left(-\dfrac{167}{18}\right)\times\left(-19\right)}{-\dfrac{58}{17}}\times\left(-15-\dfrac{253}{6}\right)\times\left(-\dfrac{69}{17}\right)\times\left(-\dfrac{190}{3}\right)\times\dfrac{253}{6}\times\dfrac{-2}{-\dfrac{28}{3}+\dfrac{253}{6}}\times\left(-15\right)\times\left(-\dfrac{28}{3}\right)\times\left(-\dfrac{91}{2}\right)\times\dfrac{253}{6}=-\dfrac{1.2952388172331E+33}{2133932579789184}\) . Voici le détail :
\begin{eqnarray*}
X &=&-\dfrac{58}{17}-\dfrac{15}{-19}-19+13+\dfrac{-13+\left(-13\right)\times\left(0+\dfrac{167}{18}\right)+\left(-13\right)\times\dfrac{253}{6}\times\left(-\dfrac{167}{18}+\dfrac{91}{2}-\dfrac{315}{13}\right)\times\left(-\dfrac{167}{18}\right)\times\left(-19\right)\times\left(-\dfrac{167}{18}\right)\times\left(-19\right)}{-\dfrac{58}{17}}\times\left(-15-\dfrac{253}{6}\right)\times\left(-\dfrac{69}{17}\right)\times\left(-\dfrac{190}{3}\right)\times\dfrac{253}{6}\times\dfrac{-2}{-\dfrac{28}{3}+\dfrac{253}{6}}\times\left(-15\right)\times\left(-\dfrac{28}{3}\right)\times\left(-\dfrac{91}{2}\right)\times\dfrac{253}{6}\\&=&-\dfrac{58}{17}-\dfrac{15}{-19}-19+13+\dfrac{-13+\left(-13\right)\times\dfrac{167}{18}+\left(-13\right)\times\dfrac{253}{6}\times\left(-\dfrac{167}{18}+\dfrac{91}{2}-\dfrac{315}{13}\right)\times\left(-\dfrac{167}{18}\right)\times\left(-19\right)\times\left(-\dfrac{167}{18}\right)\times\left(-19\right)}{-\dfrac{58}{17}}\times\left(-15-\dfrac{253}{6}\right)\times\left(-\dfrac{69}{17}\right)\times\left(-\dfrac{190}{3}\right)\times\dfrac{253}{6}\times\dfrac{-2}{-\dfrac{28}{3}+\dfrac{253}{6}}\times\left(-15\right)\times\left(-\dfrac{28}{3}\right)\times\left(-\dfrac{91}{2}\right)\times\dfrac{253}{6}\\&=&-\dfrac{58}{17}-\dfrac{15}{-19}-19+13+\dfrac{-13+\left(-13\right)\times\dfrac{167}{18}+\left(-\dfrac{3289}{6}\right)\times\left(-\dfrac{167}{18}+\dfrac{91}{2}-\dfrac{315}{13}\right)\times\left(-\dfrac{167}{18}\right)\times\left(-19\right)\times\left(-\dfrac{167}{18}\right)\times\left(-19\right)}{-\dfrac{58}{17}}\times\left(-15-\dfrac{253}{6}\right)\times\left(-\dfrac{69}{17}\right)\times\left(-\dfrac{190}{3}\right)\times\dfrac{253}{6}\times\dfrac{-2}{-\dfrac{28}{3}+\dfrac{253}{6}}\times\left(-15\right)\times\left(-\dfrac{28}{3}\right)\times\left(-\dfrac{91}{2}\right)\times\dfrac{253}{6}\\&=&-\dfrac{58}{17}-\dfrac{15}{-19}-19+13+\dfrac{-13+\left(-13\right)\times\dfrac{167}{18}+\left(-\dfrac{3289}{6}\right)\times\left(\dfrac{326}{9}-\dfrac{315}{13}\right)\times\left(-\dfrac{167}{18}\right)\times\left(-19\right)\times\left(-\dfrac{167}{18}\right)\times\left(-19\right)}{-\dfrac{58}{17}}\times\left(-15-\dfrac{253}{6}\right)\times\left(-\dfrac{69}{17}\right)\times\left(-\dfrac{190}{3}\right)\times\dfrac{253}{6}\times\dfrac{-2}{-\dfrac{28}{3}+\dfrac{253}{6}}\times\left(-15\right)\times\left(-\dfrac{28}{3}\right)\times\left(-\dfrac{91}{2}\right)\times\dfrac{253}{6}\\&=&-\dfrac{58}{17}-\dfrac{15}{-19}-19+13+\dfrac{-13+\left(-13\right)\times\dfrac{167}{18}+\left(-\dfrac{3289}{6}\right)\times\dfrac{1403}{117}\times\left(-\dfrac{167}{18}\right)\times\left(-19\right)\times\left(-\dfrac{167}{18}\right)\times\left(-19\right)}{-\dfrac{58}{17}}\times\left(-15-\dfrac{253}{6}\right)\times\left(-\dfrac{69}{17}\right)\times\left(-\dfrac{190}{3}\right)\times\dfrac{253}{6}\times\dfrac{-2}{-\dfrac{28}{3}+\dfrac{253}{6}}\times\left(-15\right)\times\left(-\dfrac{28}{3}\right)\times\left(-\dfrac{91}{2}\right)\times\dfrac{253}{6}\\&=&-\dfrac{58}{17}-\dfrac{15}{-19}-19+13+\dfrac{-13+\left(-13\right)\times\dfrac{167}{18}+\left(-\dfrac{3289}{6}\right)\times\dfrac{1403}{117}\times\dfrac{3173}{18}\times\left(-\dfrac{167}{18}\right)\times\left(-19\right)}{-\dfrac{58}{17}}\times\left(-15-\dfrac{253}{6}\right)\times\left(-\dfrac{69}{17}\right)\times\left(-\dfrac{190}{3}\right)\times\dfrac{253}{6}\times\dfrac{-2}{-\dfrac{28}{3}+\dfrac{253}{6}}\times\left(-15\right)\times\left(-\dfrac{28}{3}\right)\times\left(-\dfrac{91}{2}\right)\times\dfrac{253}{6}\\&=&-\dfrac{58}{17}-\dfrac{15}{-19}-19+13+\dfrac{-13+\left(-13\right)\times\dfrac{167}{18}+\left(-\dfrac{3289}{6}\right)\times\dfrac{1403}{117}\times\left(-\dfrac{529891}{324}\right)\times\left(-19\right)}{-\dfrac{58}{17}}\times\left(-15-\dfrac{253}{6}\right)\times\left(-\dfrac{69}{17}\right)\times\left(-\dfrac{190}{3}\right)\times\dfrac{253}{6}\times\dfrac{-2}{-\dfrac{28}{3}+\dfrac{253}{6}}\times\left(-15\right)\times\left(-\dfrac{28}{3}\right)\times\left(-\dfrac{91}{2}\right)\times\dfrac{253}{6}\\&=&-\dfrac{58}{17}-\dfrac{15}{-19}-19+13+\dfrac{-13+\left(-13\right)\times\dfrac{167}{18}+\left(-\dfrac{3289}{6}\right)\times\dfrac{1403}{117}\times\left(-\dfrac{529891}{324}\right)\times\left(-19\right)}{-\dfrac{58}{17}}\times\left(-15-\dfrac{253}{6}\right)\times\left(-\dfrac{69}{17}\right)\times\left(-\dfrac{190}{3}\right)\times\dfrac{253}{6}\times\dfrac{-2}{\dfrac{197}{6}}\times\left(-15\right)\times\left(-\dfrac{28}{3}\right)\times\left(-\dfrac{91}{2}\right)\times\dfrac{253}{6}\\&=&-\dfrac{58}{17}-\dfrac{15}{-19}-19+13+\dfrac{-13-\dfrac{2171}{18}+\left(-\dfrac{3289}{6}\right)\times\dfrac{1403}{117}\times\left(-\dfrac{529891}{324}\right)\times\left(-19\right)}{-\dfrac{58}{17}}\times\left(-15-\dfrac{253}{6}\right)\times\left(-\dfrac{69}{17}\right)\times\left(-\dfrac{190}{3}\right)\times\dfrac{253}{6}\times\dfrac{-2}{\dfrac{197}{6}}\times\left(-15\right)\times\left(-\dfrac{28}{3}\right)\times\left(-\dfrac{91}{2}\right)\times\dfrac{253}{6}\\&=&-\dfrac{58}{17}-\dfrac{15}{-19}-19+13+\dfrac{-13-\dfrac{2171}{18}+\left(-\dfrac{354959}{54}\right)\times\left(-\dfrac{529891}{324}\right)\times\left(-19\right)}{-\dfrac{58}{17}}\times\left(-15-\dfrac{253}{6}\right)\times\left(-\dfrac{69}{17}\right)\times\left(-\dfrac{190}{3}\right)\times\dfrac{253}{6}\times\dfrac{-2}{\dfrac{197}{6}}\times\left(-15\right)\times\left(-\dfrac{28}{3}\right)\times\left(-\dfrac{91}{2}\right)\times\dfrac{253}{6}\\&=&-\dfrac{58}{17}-\dfrac{15}{-19}-19+13+\dfrac{-13-\dfrac{2171}{18}+\dfrac{188089579469}{17496}\times\left(-19\right)}{-\dfrac{58}{17}}\times\left(-15-\dfrac{253}{6}\right)\times\left(-\dfrac{69}{17}\right)\times\left(-\dfrac{190}{3}\right)\times\dfrac{253}{6}\times\dfrac{-2}{\dfrac{197}{6}}\times\left(-15\right)\times\left(-\dfrac{28}{3}\right)\times\left(-\dfrac{91}{2}\right)\times\dfrac{253}{6}\\&=&-\dfrac{58}{17}-\dfrac{15}{-19}-19+13+\dfrac{-13-\dfrac{2171}{18}-\dfrac{3573702009911}{17496}}{-\dfrac{58}{17}}\times\left(-15-\dfrac{253}{6}\right)\times\left(-\dfrac{69}{17}\right)\times\left(-\dfrac{190}{3}\right)\times\dfrac{253}{6}\times\dfrac{-2}{\dfrac{197}{6}}\times\left(-15\right)\times\left(-\dfrac{28}{3}\right)\times\left(-\dfrac{91}{2}\right)\times\dfrac{253}{6}\\&=&-\dfrac{58}{17}-\dfrac{15}{-19}-19+13+\dfrac{-13-\dfrac{2171}{18}-\dfrac{3573702009911}{17496}}{-\dfrac{58}{17}}\times\left(-15-\dfrac{253}{6}\right)\times\left(-\dfrac{69}{17}\right)\times\left(-\dfrac{190}{3}\right)\times\dfrac{253}{6}\times\left(-\dfrac{12}{197}\right)\times\left(-15\right)\times\left(-\dfrac{28}{3}\right)\times\left(-\dfrac{91}{2}\right)\times\dfrac{253}{6}\\&=&-\dfrac{58}{17}-\dfrac{15}{-19}-19+13+\dfrac{-\dfrac{2405}{18}-\dfrac{3573702009911}{17496}}{-\dfrac{58}{17}}\times\left(-15-\dfrac{253}{6}\right)\times\left(-\dfrac{69}{17}\right)\times\left(-\dfrac{190}{3}\right)\times\dfrac{253}{6}\times\left(-\dfrac{12}{197}\right)\times\left(-15\right)\times\left(-\dfrac{28}{3}\right)\times\left(-\dfrac{91}{2}\right)\times\dfrac{253}{6}\\&=&-\dfrac{58}{17}-\dfrac{15}{-19}-19+13+\dfrac{-\dfrac{64326678256278}{314928}}{-\dfrac{58}{17}}\times\left(-15-\dfrac{253}{6}\right)\times\left(-\dfrac{69}{17}\right)\times\left(-\dfrac{190}{3}\right)\times\dfrac{253}{6}\times\left(-\dfrac{12}{197}\right)\times\left(-15\right)\times\left(-\dfrac{28}{3}\right)\times\left(-\dfrac{91}{2}\right)\times\dfrac{253}{6}\\&=&-\dfrac{58}{17}-\dfrac{15}{-19}-19+13+\dfrac{-\dfrac{64326678256278}{314928}}{-\dfrac{58}{17}}\times\left(-15-\dfrac{253}{6}\right)\times\left(-\dfrac{69}{17}\right)\times\left(-\dfrac{190}{3}\right)\times\dfrac{253}{6}\times\dfrac{180}{197}\times\left(-\dfrac{28}{3}\right)\times\left(-\dfrac{91}{2}\right)\times\dfrac{253}{6}\\&=&-\dfrac{58}{17}-\dfrac{15}{-19}-19+13+\dfrac{-\dfrac{64326678256278}{314928}}{-\dfrac{58}{17}}\times\left(-15-\dfrac{253}{6}\right)\times\left(-\dfrac{69}{17}\right)\times\left(-\dfrac{190}{3}\right)\times\dfrac{253}{6}\times\left(-\dfrac{1680}{197}\right)\times\left(-\dfrac{91}{2}\right)\times\dfrac{253}{6}\\&=&-\dfrac{58}{17}-\dfrac{15}{-19}-19+13+\dfrac{-\dfrac{64326678256278}{314928}}{-\dfrac{58}{17}}\times\left(-15-\dfrac{253}{6}\right)\times\left(-\dfrac{69}{17}\right)\times\left(-\dfrac{190}{3}\right)\times\dfrac{253}{6}\times\dfrac{76440}{197}\times\dfrac{253}{6}\\&=&-\dfrac{58}{17}+\dfrac{15}{19}-19+13+\dfrac{-\dfrac{64326678256278}{314928}}{-\dfrac{58}{17}}\times\left(-15-\dfrac{253}{6}\right)\times\left(-\dfrac{69}{17}\right)\times\left(-\dfrac{190}{3}\right)\times\dfrac{253}{6}\times\dfrac{76440}{197}\times\dfrac{253}{6}\\&=&-\dfrac{58}{17}+\dfrac{15}{19}-19+13+\left(\dfrac{1093553530356726}{18265824}\right)\times\left(-15-\dfrac{253}{6}\right)\times\left(-\dfrac{69}{17}\right)\times\left(-\dfrac{190}{3}\right)\times\dfrac{253}{6}\times\dfrac{76440}{197}\times\dfrac{253}{6}\\&=&-\dfrac{58}{17}+\dfrac{15}{19}-19+13+\left(\dfrac{1093553530356726}{18265824}\right)\times-\dfrac{343}{6}\times\left(-\dfrac{69}{17}\right)\times\left(-\dfrac{190}{3}\right)\times\dfrac{253}{6}\times\dfrac{76440}{197}\times\dfrac{253}{6}\\&=&-\dfrac{58}{17}+\dfrac{15}{19}-19+13+\left(\dfrac{1093553530356726}{18265824}\right)\times-\dfrac{343}{6}\times\dfrac{4370}{17}\times\dfrac{253}{6}\times\dfrac{76440}{197}\times\dfrac{253}{6}\\&=&-\dfrac{58}{17}+\dfrac{15}{19}-19+13+\left(\dfrac{1093553530356726}{18265824}\right)\times-\dfrac{343}{6}\times\dfrac{552805}{51}\times\dfrac{76440}{197}\times\dfrac{253}{6}\\&=&-\dfrac{58}{17}+\dfrac{15}{19}-19+13+\left(\dfrac{1093553530356726}{18265824}\right)\times-\dfrac{343}{6}\times\dfrac{42256414200}{10047}\times\dfrac{253}{6}\\&=&-\dfrac{847}{323}-19+13+\left(\dfrac{1093553530356726}{18265824}\right)\times-\dfrac{343}{6}\times\dfrac{42256414200}{10047}\times\dfrac{253}{6}\\&=&-\dfrac{847}{323}-19+13+\left(-\dfrac{375088860912357018}{109594944}\right)\times\dfrac{42256414200}{10047}\times\dfrac{253}{6}\\&=&-\dfrac{847}{323}-19+13+\left(-\dfrac{1.5849910268519E+28}{1101100402368}\right)\times\dfrac{253}{6}\\&=&-\dfrac{847}{323}-19+13-\dfrac{4.0100272979352E+30}{6606602414208}\\&=&-\dfrac{6984}{323}+13-\dfrac{4.0100272979352E+30}{6606602414208}\\&=&-\dfrac{2785}{323}-\dfrac{4.0100272979352E+30}{6606602414208}\\&=&-\dfrac{1.2952388172331E+33}{2133932579789184}\\
\end{eqnarray*}