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Exercice

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 \[6\times\left(\dfrac{3}{2}-\dfrac{\dfrac{6-\left(-\dfrac{88}{3}\right)\times6\times\dfrac{3}{2}-\dfrac{134}{5}+2}{\dfrac{\dfrac{\dfrac{4}{-5}}{\dfrac{47}{8}}}{\dfrac{134}{5}}+\dfrac{\dfrac{\dfrac{4}{-2}}{-\dfrac{88}{3}}}{4}-\dfrac{130}{9}-\dfrac{116}{11}-\dfrac{67}{4}+6-\dfrac{25}{11}}}{6\times\left(-4\right)\times4\times\left(-2\right)}+5-\dfrac{\dfrac{-\dfrac{88}{3}}{-8}}{6}\right)\times\left(-8\right)\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=6\times\left(\dfrac{3}{2}-\dfrac{\dfrac{6-\left(-\dfrac{88}{3}\right)\times6\times\dfrac{3}{2}-\dfrac{134}{5}+2}{\dfrac{\dfrac{\dfrac{4}{-5}}{\dfrac{47}{8}}}{\dfrac{134}{5}}+\dfrac{\dfrac{\dfrac{4}{-2}}{-\dfrac{88}{3}}}{4}-\dfrac{130}{9}-\dfrac{116}{11}-\dfrac{67}{4}+6-\dfrac{25}{11}}}{6\times\left(-4\right)\times4\times\left(-2\right)}+5-\dfrac{\dfrac{-\dfrac{88}{3}}{-8}}{6}\right)\times\left(-8\right)=-\dfrac{81939140477263872}{288234132341760}\) . Voici le détail : \begin{eqnarray*} X &=&6\times\left(\dfrac{3}{2}-\dfrac{\dfrac{6-\left(-176\right)\times\dfrac{3}{2}-\dfrac{134}{5}+2}{\dfrac{\dfrac{\dfrac{4}{-5}}{\dfrac{47}{8}}}{\dfrac{134}{5}}+\dfrac{\dfrac{\dfrac{4}{-2}}{-\dfrac{88}{3}}}{4}-\dfrac{130}{9}-\dfrac{116}{11}-\dfrac{67}{4}+6-\dfrac{25}{11}}}{6\times\left(-4\right)\times4\times\left(-2\right)}+5-\dfrac{\dfrac{-\dfrac{88}{3}}{-8}}{6}\right)\times\left(-8\right)\\&=&6\times\left(\dfrac{3}{2}-\dfrac{\dfrac{6+264-\dfrac{134}{5}+2}{\dfrac{\dfrac{\dfrac{4}{-5}}{\dfrac{47}{8}}}{\dfrac{134}{5}}+\dfrac{\dfrac{\dfrac{4}{-2}}{-\dfrac{88}{3}}}{4}-\dfrac{130}{9}-\dfrac{116}{11}-\dfrac{67}{4}+6-\dfrac{25}{11}}}{6\times\left(-4\right)\times4\times\left(-2\right)}+5-\dfrac{\dfrac{-\dfrac{88}{3}}{-8}}{6}\right)\times\left(-8\right)\\&=&6\times\left(\dfrac{3}{2}-\dfrac{\dfrac{6+264-\dfrac{134}{5}+2}{\dfrac{\dfrac{-\dfrac{4}{5}}{\dfrac{47}{8}}}{\dfrac{134}{5}}+\dfrac{\dfrac{\dfrac{4}{-2}}{-\dfrac{88}{3}}}{4}-\dfrac{130}{9}-\dfrac{116}{11}-\dfrac{67}{4}+6-\dfrac{25}{11}}}{6\times\left(-4\right)\times4\times\left(-2\right)}+5-\dfrac{\dfrac{-\dfrac{88}{3}}{-8}}{6}\right)\times\left(-8\right)\\&=&6\times\left(\dfrac{3}{2}-\dfrac{\dfrac{6+264-\dfrac{134}{5}+2}{\dfrac{-\dfrac{32}{235}}{\dfrac{134}{5}}+\dfrac{\dfrac{\dfrac{4}{-2}}{-\dfrac{88}{3}}}{4}-\dfrac{130}{9}-\dfrac{116}{11}-\dfrac{67}{4}+6-\dfrac{25}{11}}}{6\times\left(-4\right)\times4\times\left(-2\right)}+5-\dfrac{\dfrac{-\dfrac{88}{3}}{-8}}{6}\right)\times\left(-8\right)\\&=&6\times\left(\dfrac{3}{2}-\dfrac{\dfrac{6+264-\dfrac{134}{5}+2}{-\dfrac{16}{3149}+\dfrac{\dfrac{\dfrac{4}{-2}}{-\dfrac{88}{3}}}{4}-\dfrac{130}{9}-\dfrac{116}{11}-\dfrac{67}{4}+6-\dfrac{25}{11}}}{6\times\left(-4\right)\times4\times\left(-2\right)}+5-\dfrac{\dfrac{-\dfrac{88}{3}}{-8}}{6}\right)\times\left(-8\right)\\&=&6\times\left(\dfrac{3}{2}-\dfrac{\dfrac{6+264-\dfrac{134}{5}+2}{-\dfrac{16}{3149}+\dfrac{\dfrac{-2}{-\dfrac{88}{3}}}{4}-\dfrac{130}{9}-\dfrac{116}{11}-\dfrac{67}{4}+6-\dfrac{25}{11}}}{6\times\left(-4\right)\times4\times\left(-2\right)}+5-\dfrac{\dfrac{-\dfrac{88}{3}}{-8}}{6}\right)\times\left(-8\right)\\&=&6\times\left(\dfrac{3}{2}-\dfrac{\dfrac{6+264-\dfrac{134}{5}+2}{-\dfrac{16}{3149}+\dfrac{\dfrac{3}{44}}{4}-\dfrac{130}{9}-\dfrac{116}{11}-\dfrac{67}{4}+6-\dfrac{25}{11}}}{6\times\left(-4\right)\times4\times\left(-2\right)}+5-\dfrac{\dfrac{-\dfrac{88}{3}}{-8}}{6}\right)\times\left(-8\right)\\&=&6\times\left(\dfrac{3}{2}-\dfrac{\dfrac{6+264-\dfrac{134}{5}+2}{-\dfrac{16}{3149}+\dfrac{3}{176}-\dfrac{130}{9}-\dfrac{116}{11}-\dfrac{67}{4}+6-\dfrac{25}{11}}}{6\times\left(-4\right)\times4\times\left(-2\right)}+5-\dfrac{\dfrac{-\dfrac{88}{3}}{-8}}{6}\right)\times\left(-8\right)\\&=&6\times\left(\dfrac{3}{2}-\dfrac{\dfrac{6+264-\dfrac{134}{5}+2}{-\dfrac{16}{3149}+\dfrac{3}{176}-\dfrac{2474}{99}-\dfrac{67}{4}+6-\dfrac{25}{11}}}{6\times\left(-4\right)\times4\times\left(-2\right)}+5-\dfrac{\dfrac{-\dfrac{88}{3}}{-8}}{6}\right)\times\left(-8\right)\\&=&6\times\left(\dfrac{3}{2}-\dfrac{\dfrac{6+264-\dfrac{134}{5}+2}{-\dfrac{16}{3149}+\dfrac{3}{176}-\dfrac{2474}{99}-\dfrac{43}{4}-\dfrac{25}{11}}}{6\times\left(-4\right)\times4\times\left(-2\right)}+5-\dfrac{\dfrac{-\dfrac{88}{3}}{-8}}{6}\right)\times\left(-8\right)\\&=&6\times\left(\dfrac{3}{2}-\dfrac{\dfrac{6+264-\dfrac{134}{5}+2}{-\dfrac{16}{3149}+\dfrac{3}{176}-\dfrac{2474}{99}-\dfrac{573}{44}}}{6\times\left(-4\right)\times4\times\left(-2\right)}+5-\dfrac{\dfrac{-\dfrac{88}{3}}{-8}}{6}\right)\times\left(-8\right)\\&=&6\times\left(\dfrac{3}{2}-\dfrac{\dfrac{6+264-\dfrac{134}{5}+2}{-\dfrac{16}{3149}+\dfrac{3}{176}-\dfrac{2474}{99}-\dfrac{573}{44}}}{\left(-24\right)\times4\times\left(-2\right)}+5-\dfrac{\dfrac{-\dfrac{88}{3}}{-8}}{6}\right)\times\left(-8\right)\\&=&6\times\left(\dfrac{3}{2}-\dfrac{\dfrac{6+264-\dfrac{134}{5}+2}{-\dfrac{16}{3149}+\dfrac{3}{176}-\dfrac{2474}{99}-\dfrac{573}{44}}}{\left(-96\right)\times\left(-2\right)}+5-\dfrac{\dfrac{-\dfrac{88}{3}}{-8}}{6}\right)\times\left(-8\right)\\&=&6\times\left(\dfrac{3}{2}-\dfrac{\dfrac{270-\dfrac{134}{5}+2}{-\dfrac{16}{3149}+\dfrac{3}{176}-\dfrac{2474}{99}-\dfrac{573}{44}}}{\left(-96\right)\times\left(-2\right)}+5-\dfrac{\dfrac{-\dfrac{88}{3}}{-8}}{6}\right)\times\left(-8\right)\\&=&6\times\left(\dfrac{3}{2}-\dfrac{\dfrac{\dfrac{1216}{5}+2}{-\dfrac{16}{3149}+\dfrac{3}{176}-\dfrac{2474}{99}-\dfrac{573}{44}}}{\left(-96\right)\times\left(-2\right)}+5-\dfrac{\dfrac{-\dfrac{88}{3}}{-8}}{6}\right)\times\left(-8\right)\\&=&6\times\left(\dfrac{3}{2}-\dfrac{\dfrac{\dfrac{1226}{5}}{-\dfrac{16}{3149}+\dfrac{3}{176}-\dfrac{2474}{99}-\dfrac{573}{44}}}{\left(-96\right)\times\left(-2\right)}+5-\dfrac{\dfrac{-\dfrac{88}{3}}{-8}}{6}\right)\times\left(-8\right)\\&=&6\times\left(\dfrac{3}{2}-\dfrac{\dfrac{\dfrac{1226}{5}}{\dfrac{6631}{554224}-\dfrac{2474}{99}-\dfrac{573}{44}}}{\left(-96\right)\times\left(-2\right)}+5-\dfrac{\dfrac{-\dfrac{88}{3}}{-8}}{6}\right)\times\left(-8\right)\\&=&6\times\left(\dfrac{3}{2}-\dfrac{\dfrac{\dfrac{1226}{5}}{-\dfrac{124590337}{4988016}-\dfrac{573}{44}}}{\left(-96\right)\times\left(-2\right)}+5-\dfrac{\dfrac{-\dfrac{88}{3}}{-8}}{6}\right)\times\left(-8\right)\\&=&6\times\left(\dfrac{3}{2}-\dfrac{\dfrac{\dfrac{1226}{5}}{-\dfrac{8340107996}{219472704}}}{\left(-96\right)\times\left(-2\right)}+5-\dfrac{\dfrac{-\dfrac{88}{3}}{-8}}{6}\right)\times\left(-8\right)\\&=&6\times\left(\dfrac{3}{2}-\dfrac{\dfrac{\dfrac{1226}{5}}{-\dfrac{8340107996}{219472704}}}{192}+5-\dfrac{\dfrac{-\dfrac{88}{3}}{-8}}{6}\right)\times\left(-8\right)\\&=&6\times\left(\dfrac{3}{2}-\dfrac{-\dfrac{269073535104}{41700539980}}{192}+5-\dfrac{\dfrac{-\dfrac{88}{3}}{-8}}{6}\right)\times\left(-8\right)\\&=&6\times\left(\dfrac{3}{2}+\dfrac{269073535104}{8006503676160}+5-\dfrac{\dfrac{-\dfrac{88}{3}}{-8}}{6}\right)\times\left(-8\right)\\&=&6\times\left(\dfrac{3}{2}+\dfrac{269073535104}{8006503676160}+5-\dfrac{\dfrac{11}{3}}{6}\right)\times\left(-8\right)\\&=&6\times\left(\dfrac{3}{2}+\dfrac{269073535104}{8006503676160}+5-\dfrac{11}{18}\right)\times\left(-8\right)\\&=&6\times\left(\dfrac{24557658098688}{16013007352320}+5-\dfrac{11}{18}\right)\times\left(-8\right)\\&=&6\times\left(\dfrac{104622694860288}{16013007352320}-\dfrac{11}{18}\right)\times\left(-8\right)\\&=&6\times\dfrac{1707065426609664}{288234132341760}\times\left(-8\right)\\&=&\dfrac{10242392559657984}{288234132341760}\times\left(-8\right)\\&=&-\dfrac{81939140477263872}{288234132341760}\\ \end{eqnarray*}