L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
Si vous regénérez la page (F5) les valeurs seront changées.
La correction se trouve en bas de page.
Exercice
Calculer \[\left(-5\right)\times\left(\dfrac{-4}{-4}-\dfrac{\dfrac{\dfrac{-5}{2}}{-\dfrac{33}{4}}}{\dfrac{33}{10}}-\left(-\dfrac{7}{8}\right)\times\dfrac{1}{-4}\times\left(-4\right)\right)\times\dfrac{33}{10}\times1\times\dfrac{\dfrac{\dfrac{4}{4}}{\dfrac{26}{3}\times\left(\dfrac{43}{4}+4\right)}}{4}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\left(-5\right)\times\left(\dfrac{-4}{-4}-\dfrac{\dfrac{\dfrac{-5}{2}}{-\dfrac{33}{4}}}{\dfrac{33}{10}}-\left(-\dfrac{7}{8}\right)\times\dfrac{1}{-4}\times\left(-4\right)\right)\times\dfrac{33}{10}\times1\times\dfrac{\dfrac{\dfrac{4}{4}}{\dfrac{26}{3}\times\left(\dfrac{43}{4}+4\right)}}{4}=-\dfrac{1195}{20768}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(-5\right)\times\left(\dfrac{-4}{-4}-\dfrac{\dfrac{\dfrac{-5}{2}}{-\dfrac{33}{4}}}{\dfrac{33}{10}}-\left(-\dfrac{7}{8}\right)\times\left(-\dfrac{1}{4}\right)\times\left(-4\right)\right)\times\dfrac{33}{10}\times1\times\dfrac{\dfrac{\dfrac{4}{4}}{\dfrac{26}{3}\times\left(\dfrac{43}{4}+4\right)}}{4}\\&=&\left(-5\right)\times\left(\dfrac{-4}{-4}-\dfrac{\dfrac{\dfrac{-5}{2}}{-\dfrac{33}{4}}}{\dfrac{33}{10}}-\left(-\dfrac{7}{8}\right)\times\left(-\dfrac{1}{4}\right)\times\left(-4\right)\right)\times\dfrac{33}{10}\times1\times\dfrac{\dfrac{\dfrac{4}{4}}{\dfrac{26}{3}\times\dfrac{59}{4}}}{4}\\&=&\left(-5\right)\times\left(\dfrac{-4}{-4}-\dfrac{\dfrac{\dfrac{-5}{2}}{-\dfrac{33}{4}}}{\dfrac{33}{10}}-\left(-\dfrac{7}{8}\right)\times1\right)\times\dfrac{33}{10}\times1\times\dfrac{\dfrac{\dfrac{4}{4}}{\dfrac{26}{3}\times\dfrac{59}{4}}}{4}\\&=&\left(-5\right)\times\left(\dfrac{-4}{-4}-\dfrac{\dfrac{\dfrac{-5}{2}}{-\dfrac{33}{4}}}{\dfrac{33}{10}}-\left(-\dfrac{7}{8}\right)\times1\right)\times\dfrac{33}{10}\times1\times\dfrac{\dfrac{\dfrac{4}{4}}{\dfrac{767}{6}}}{4}\\&=&\left(-5\right)\times\left(1-\dfrac{\dfrac{\dfrac{-5}{2}}{-\dfrac{33}{4}}}{\dfrac{33}{10}}-\left(-\dfrac{7}{8}\right)\times1\right)\times\dfrac{33}{10}\times1\times\dfrac{\dfrac{\dfrac{4}{4}}{\dfrac{767}{6}}}{4}\\&=&\left(-5\right)\times\left(1-\dfrac{\dfrac{-\dfrac{5}{2}}{-\dfrac{33}{4}}}{\dfrac{33}{10}}-\left(-\dfrac{7}{8}\right)\times1\right)\times\dfrac{33}{10}\times1\times\dfrac{\dfrac{\dfrac{4}{4}}{\dfrac{767}{6}}}{4}\\&=&\left(-5\right)\times\left(1-\dfrac{\dfrac{10}{33}}{\dfrac{33}{10}}-\left(-\dfrac{7}{8}\right)\times1\right)\times\dfrac{33}{10}\times1\times\dfrac{\dfrac{\dfrac{4}{4}}{\dfrac{767}{6}}}{4}\\&=&\left(-5\right)\times\left(1-\dfrac{100}{1089}-\left(-\dfrac{7}{8}\right)\times1\right)\times\dfrac{33}{10}\times1\times\dfrac{\dfrac{\dfrac{4}{4}}{\dfrac{767}{6}}}{4}\\&=&\left(-5\right)\times\left(1-\dfrac{100}{1089}+\dfrac{7}{8}\right)\times\dfrac{33}{10}\times1\times\dfrac{\dfrac{\dfrac{4}{4}}{\dfrac{767}{6}}}{4}\\&=&\left(-5\right)\times\left(1-\dfrac{100}{1089}+\dfrac{7}{8}\right)\times\dfrac{33}{10}\times1\times\dfrac{\dfrac{1}{\dfrac{767}{6}}}{4}\\&=&\left(-5\right)\times\left(1-\dfrac{100}{1089}+\dfrac{7}{8}\right)\times\dfrac{33}{10}\times1\times\dfrac{\dfrac{6}{767}}{4}\\&=&\left(-5\right)\times\left(1-\dfrac{100}{1089}+\dfrac{7}{8}\right)\times\dfrac{33}{10}\times1\times\dfrac{3}{1534}\\&=&\left(-5\right)\times\left(\dfrac{989}{1089}+\dfrac{7}{8}\right)\times\dfrac{33}{10}\times1\times\dfrac{3}{1534}\\&=&\left(-5\right)\times\dfrac{15535}{8712}\times\dfrac{33}{10}\times1\times\dfrac{3}{1534}\\&=&\left(-5\right)\times\dfrac{15535}{8712}\times\dfrac{33}{10}\times\dfrac{3}{1534}\\&=&\left(-5\right)\times\dfrac{15535}{8712}\times\dfrac{99}{15340}\\&=&\left(-\dfrac{77675}{8712}\right)\times\dfrac{99}{15340}\\&=&-\dfrac{1195}{20768}\\
\end{eqnarray*}