L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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Exercice
Calculer \[\left(\left(0\times\dfrac{18}{5}\times0-1+3+0+\dfrac{18}{5}\right)-\left(\dfrac{17}{2}+\dfrac{1}{6}\right)\times\dfrac{17}{2}-0\right)+\dfrac{1}{6}-\left(\dfrac{18}{5}-\dfrac{17}{2}-\left(\dfrac{18}{5}-\dfrac{18}{5}+\dfrac{1}{6}+\dfrac{17}{2}+\dfrac{33}{2}\right)\right)\]
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Exercice
On a \( X=\left(\left(0\times\dfrac{18}{5}\times0-1+3+0+\dfrac{18}{5}\right)-\left(\dfrac{17}{2}+\dfrac{1}{6}\right)\times\dfrac{17}{2}-0\right)+\dfrac{1}{6}-\left(\dfrac{18}{5}-\dfrac{17}{2}-\left(\dfrac{18}{5}-\dfrac{18}{5}+\dfrac{1}{6}+\dfrac{17}{2}+\dfrac{33}{2}\right)\right)=-\dfrac{227}{6}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(\left(0\times0-1+3+0+\dfrac{18}{5}\right)-\left(\dfrac{17}{2}+\dfrac{1}{6}\right)\times\dfrac{17}{2}-0\right)+\dfrac{1}{6}-\left(\dfrac{18}{5}-\dfrac{17}{2}-\left(\dfrac{18}{5}-\dfrac{18}{5}+\dfrac{1}{6}+\dfrac{17}{2}+\dfrac{33}{2}\right)\right)\\&=&\left(\left(0-1+3+0+\dfrac{18}{5}\right)-\left(\dfrac{17}{2}+\dfrac{1}{6}\right)\times\dfrac{17}{2}-0\right)+\dfrac{1}{6}-\left(\dfrac{18}{5}-\dfrac{17}{2}-\left(\dfrac{18}{5}-\dfrac{18}{5}+\dfrac{1}{6}+\dfrac{17}{2}+\dfrac{33}{2}\right)\right)\\&=&\left(\left(0-1+3+\dfrac{18}{5}\right)-\left(\dfrac{17}{2}+\dfrac{1}{6}\right)\times\dfrac{17}{2}-0\right)+\dfrac{1}{6}-\left(\dfrac{18}{5}-\dfrac{17}{2}-\left(\dfrac{18}{5}-\dfrac{18}{5}+\dfrac{1}{6}+\dfrac{17}{2}+\dfrac{33}{2}\right)\right)\\&=&\left(\left(0-1+\dfrac{33}{5}\right)-\left(\dfrac{17}{2}+\dfrac{1}{6}\right)\times\dfrac{17}{2}-0\right)+\dfrac{1}{6}-\left(\dfrac{18}{5}-\dfrac{17}{2}-\left(\dfrac{18}{5}-\dfrac{18}{5}+\dfrac{1}{6}+\dfrac{17}{2}+\dfrac{33}{2}\right)\right)\\&=&\left(\left(0-1+\dfrac{33}{5}\right)-\dfrac{26}{3}\times\dfrac{17}{2}-0\right)+\dfrac{1}{6}-\left(\dfrac{18}{5}-\dfrac{17}{2}-\left(\dfrac{18}{5}-\dfrac{18}{5}+\dfrac{1}{6}+\dfrac{17}{2}+\dfrac{33}{2}\right)\right)\\&=&\left(\left(0-1+\dfrac{33}{5}\right)-\dfrac{26}{3}\times\dfrac{17}{2}-0\right)+\dfrac{1}{6}-\left(\dfrac{18}{5}-\dfrac{17}{2}-\left(0+\dfrac{1}{6}+\dfrac{17}{2}+\dfrac{33}{2}\right)\right)\\&=&\left(\left(0-1+\dfrac{33}{5}\right)-\dfrac{26}{3}\times\dfrac{17}{2}-0\right)+\dfrac{1}{6}-\left(\dfrac{18}{5}-\dfrac{17}{2}-\left(\dfrac{1}{6}+\dfrac{17}{2}+\dfrac{33}{2}\right)\right)\\&=&\left(\left(-1+\dfrac{33}{5}\right)-\dfrac{26}{3}\times\dfrac{17}{2}-0\right)+\dfrac{1}{6}-\left(\dfrac{18}{5}-\dfrac{17}{2}-\left(\dfrac{1}{6}+\dfrac{17}{2}+\dfrac{33}{2}\right)\right)\\&=&\left(\dfrac{28}{5}-\dfrac{26}{3}\times\dfrac{17}{2}-0\right)+\dfrac{1}{6}-\left(\dfrac{18}{5}-\dfrac{17}{2}-\left(\dfrac{1}{6}+\dfrac{17}{2}+\dfrac{33}{2}\right)\right)\\&=&\left(\dfrac{28}{5}-\dfrac{221}{3}-0\right)+\dfrac{1}{6}-\left(\dfrac{18}{5}-\dfrac{17}{2}-\left(\dfrac{1}{6}+\dfrac{17}{2}+\dfrac{33}{2}\right)\right)\\&=&\left(\dfrac{28}{5}-\dfrac{221}{3}-0\right)+\dfrac{1}{6}-\left(\dfrac{18}{5}-\dfrac{17}{2}-\left(\dfrac{26}{3}+\dfrac{33}{2}\right)\right)\\&=&\left(\dfrac{28}{5}-\dfrac{221}{3}-0\right)+\dfrac{1}{6}-\left(\dfrac{18}{5}-\dfrac{17}{2}-\dfrac{151}{6}\right)\\&=&\left(-\dfrac{1021}{15}-0\right)+\dfrac{1}{6}-\left(\dfrac{18}{5}-\dfrac{17}{2}-\dfrac{151}{6}\right)\\&=&-\dfrac{1021}{15}+\dfrac{1}{6}-\left(\dfrac{18}{5}-\dfrac{17}{2}-\dfrac{151}{6}\right)\\&=&-\dfrac{1021}{15}+\dfrac{1}{6}-\left(-\dfrac{49}{10}-\dfrac{151}{6}\right)\\&=&-\dfrac{1021}{15}+\dfrac{1}{6}+\dfrac{451}{15}\\&=&-\dfrac{679}{10}+\dfrac{451}{15}\\&=&-\dfrac{227}{6}\\
\end{eqnarray*}