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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 \[\dfrac{\dfrac{\dfrac{11+4}{12}}{\left(-5+\dfrac{125}{8}-\dfrac{144}{11}-5+8\right)-\left(-\dfrac{47}{8}+\dfrac{\dfrac{-5}{\dfrac{125}{8}}}{-7}-\dfrac{47}{8}\right)+\dfrac{46}{3}}}{-1}+\dfrac{\dfrac{-\dfrac{47}{8}}{-\dfrac{47}{8}}}{\dfrac{\dfrac{\dfrac{8}{12}}{\left(-\dfrac{46}{3}\right)\times8}}{11+\dfrac{125}{8}}\times11\times\left(-5\right)}+8\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=\dfrac{\dfrac{\dfrac{11+4}{12}}{\left(-5+\dfrac{125}{8}-\dfrac{144}{11}-5+8\right)-\left(-\dfrac{47}{8}+\dfrac{\dfrac{-5}{\dfrac{125}{8}}}{-7}-\dfrac{47}{8}\right)+\dfrac{46}{3}}}{-1}+\dfrac{\dfrac{-\dfrac{47}{8}}{-\dfrac{47}{8}}}{\dfrac{\dfrac{\dfrac{8}{12}}{\left(-\dfrac{46}{3}\right)\times8}}{11+\dfrac{125}{8}}\times11\times\left(-5\right)}+8=\dfrac{6797711357}{70059715}\) . Voici le détail : \begin{eqnarray*} X &=&\dfrac{\dfrac{\dfrac{11+4}{12}}{\left(-5+\dfrac{223}{88}-5+8\right)-\left(-\dfrac{47}{8}+\dfrac{\dfrac{-5}{\dfrac{125}{8}}}{-7}-\dfrac{47}{8}\right)+\dfrac{46}{3}}}{-1}+\dfrac{\dfrac{-\dfrac{47}{8}}{-\dfrac{47}{8}}}{\dfrac{\dfrac{\dfrac{8}{12}}{\left(-\dfrac{46}{3}\right)\times8}}{11+\dfrac{125}{8}}\times11\times\left(-5\right)}+8\\&=&\dfrac{\dfrac{\dfrac{11+4}{12}}{\left(-5-\dfrac{217}{88}+8\right)-\left(-\dfrac{47}{8}+\dfrac{\dfrac{-5}{\dfrac{125}{8}}}{-7}-\dfrac{47}{8}\right)+\dfrac{46}{3}}}{-1}+\dfrac{\dfrac{-\dfrac{47}{8}}{-\dfrac{47}{8}}}{\dfrac{\dfrac{\dfrac{8}{12}}{\left(-\dfrac{46}{3}\right)\times8}}{11+\dfrac{125}{8}}\times11\times\left(-5\right)}+8\\&=&\dfrac{\dfrac{\dfrac{11+4}{12}}{\left(-5+\dfrac{487}{88}\right)-\left(-\dfrac{47}{8}+\dfrac{\dfrac{-5}{\dfrac{125}{8}}}{-7}-\dfrac{47}{8}\right)+\dfrac{46}{3}}}{-1}+\dfrac{\dfrac{-\dfrac{47}{8}}{-\dfrac{47}{8}}}{\dfrac{\dfrac{\dfrac{8}{12}}{\left(-\dfrac{46}{3}\right)\times8}}{11+\dfrac{125}{8}}\times11\times\left(-5\right)}+8\\&=&\dfrac{\dfrac{\dfrac{11+4}{12}}{\left(-5+\dfrac{487}{88}\right)-\left(-\dfrac{47}{8}+\dfrac{-\dfrac{8}{25}}{-7}-\dfrac{47}{8}\right)+\dfrac{46}{3}}}{-1}+\dfrac{\dfrac{-\dfrac{47}{8}}{-\dfrac{47}{8}}}{\dfrac{\dfrac{\dfrac{8}{12}}{\left(-\dfrac{46}{3}\right)\times8}}{11+\dfrac{125}{8}}\times11\times\left(-5\right)}+8\\&=&\dfrac{\dfrac{\dfrac{11+4}{12}}{\left(-5+\dfrac{487}{88}\right)-\left(-\dfrac{47}{8}+\dfrac{8}{175}-\dfrac{47}{8}\right)+\dfrac{46}{3}}}{-1}+\dfrac{\dfrac{-\dfrac{47}{8}}{-\dfrac{47}{8}}}{\dfrac{\dfrac{\dfrac{8}{12}}{\left(-\dfrac{46}{3}\right)\times8}}{11+\dfrac{125}{8}}\times11\times\left(-5\right)}+8\\&=&\dfrac{\dfrac{\dfrac{11+4}{12}}{\left(-5+\dfrac{487}{88}\right)-\left(-\dfrac{47}{8}+\dfrac{8}{175}-\dfrac{47}{8}\right)+\dfrac{46}{3}}}{-1}+\dfrac{\dfrac{-\dfrac{47}{8}}{-\dfrac{47}{8}}}{\dfrac{\dfrac{\dfrac{2}{3}}{\left(-\dfrac{46}{3}\right)\times8}}{11+\dfrac{125}{8}}\times11\times\left(-5\right)}+8\\&=&\dfrac{\dfrac{\dfrac{11+4}{12}}{\left(-5+\dfrac{487}{88}\right)-\left(-\dfrac{47}{8}+\dfrac{8}{175}-\dfrac{47}{8}\right)+\dfrac{46}{3}}}{-1}+\dfrac{\dfrac{-\dfrac{47}{8}}{-\dfrac{47}{8}}}{\dfrac{\dfrac{\dfrac{2}{3}}{-\dfrac{368}{3}}}{11+\dfrac{125}{8}}\times11\times\left(-5\right)}+8\\&=&\dfrac{\dfrac{\dfrac{11+4}{12}}{\left(-5+\dfrac{487}{88}\right)-\left(-\dfrac{47}{8}+\dfrac{8}{175}-\dfrac{47}{8}\right)+\dfrac{46}{3}}}{-1}+\dfrac{\dfrac{-\dfrac{47}{8}}{-\dfrac{47}{8}}}{\dfrac{\dfrac{\dfrac{2}{3}}{-\dfrac{368}{3}}}{\dfrac{213}{8}}\times11\times\left(-5\right)}+8\\&=&\dfrac{\dfrac{\dfrac{11+4}{12}}{\dfrac{47}{88}-\left(-\dfrac{47}{8}+\dfrac{8}{175}-\dfrac{47}{8}\right)+\dfrac{46}{3}}}{-1}+\dfrac{\dfrac{-\dfrac{47}{8}}{-\dfrac{47}{8}}}{\dfrac{\dfrac{\dfrac{2}{3}}{-\dfrac{368}{3}}}{\dfrac{213}{8}}\times11\times\left(-5\right)}+8\\&=&\dfrac{\dfrac{\dfrac{11+4}{12}}{\dfrac{47}{88}-\left(-\dfrac{8161}{1400}-\dfrac{47}{8}\right)+\dfrac{46}{3}}}{-1}+\dfrac{\dfrac{-\dfrac{47}{8}}{-\dfrac{47}{8}}}{\dfrac{\dfrac{\dfrac{2}{3}}{-\dfrac{368}{3}}}{\dfrac{213}{8}}\times11\times\left(-5\right)}+8\\&=&\dfrac{\dfrac{\dfrac{11+4}{12}}{\dfrac{47}{88}+\dfrac{8193}{700}+\dfrac{46}{3}}}{-1}+\dfrac{\dfrac{-\dfrac{47}{8}}{-\dfrac{47}{8}}}{\dfrac{\dfrac{\dfrac{2}{3}}{-\dfrac{368}{3}}}{\dfrac{213}{8}}\times11\times\left(-5\right)}+8\\&=&\dfrac{\dfrac{\dfrac{11+4}{12}}{\dfrac{47}{88}+\dfrac{8193}{700}+\dfrac{46}{3}}}{-1}+\dfrac{\dfrac{-\dfrac{47}{8}}{-\dfrac{47}{8}}}{\dfrac{-\dfrac{1}{184}}{\dfrac{213}{8}}\times11\times\left(-5\right)}+8\\&=&\dfrac{\dfrac{\dfrac{11+4}{12}}{\dfrac{47}{88}+\dfrac{8193}{700}+\dfrac{46}{3}}}{-1}+\dfrac{\dfrac{-\dfrac{47}{8}}{-\dfrac{47}{8}}}{\left(-\dfrac{1}{4899}\right)\times11\times\left(-5\right)}+8\\&=&\dfrac{\dfrac{\dfrac{15}{12}}{\dfrac{47}{88}+\dfrac{8193}{700}+\dfrac{46}{3}}}{-1}+\dfrac{\dfrac{-\dfrac{47}{8}}{-\dfrac{47}{8}}}{\left(-\dfrac{1}{4899}\right)\times11\times\left(-5\right)}+8\\&=&\dfrac{\dfrac{\dfrac{15}{12}}{\dfrac{188471}{15400}+\dfrac{46}{3}}}{-1}+\dfrac{\dfrac{-\dfrac{47}{8}}{-\dfrac{47}{8}}}{\left(-\dfrac{1}{4899}\right)\times11\times\left(-5\right)}+8\\&=&\dfrac{\dfrac{\dfrac{15}{12}}{\dfrac{1273813}{46200}}}{-1}+\dfrac{\dfrac{-\dfrac{47}{8}}{-\dfrac{47}{8}}}{\left(-\dfrac{1}{4899}\right)\times11\times\left(-5\right)}+8\\&=&\dfrac{\dfrac{\dfrac{15}{12}}{\dfrac{1273813}{46200}}}{-1}+\dfrac{\dfrac{-\dfrac{47}{8}}{-\dfrac{47}{8}}}{\left(-\dfrac{11}{4899}\right)\times\left(-5\right)}+8\\&=&\dfrac{\dfrac{\dfrac{15}{12}}{\dfrac{1273813}{46200}}}{-1}+\dfrac{\dfrac{-\dfrac{47}{8}}{-\dfrac{47}{8}}}{\dfrac{55}{4899}}+8\\&=&\dfrac{\dfrac{\dfrac{5}{4}}{\dfrac{1273813}{46200}}}{-1}+\dfrac{\dfrac{-\dfrac{47}{8}}{-\dfrac{47}{8}}}{\dfrac{55}{4899}}+8\\&=&\dfrac{\dfrac{57750}{1273813}}{-1}+\dfrac{\dfrac{-\dfrac{47}{8}}{-\dfrac{47}{8}}}{\dfrac{55}{4899}}+8\\&=&-\dfrac{57750}{1273813}+\dfrac{\dfrac{-\dfrac{47}{8}}{-\dfrac{47}{8}}}{\dfrac{55}{4899}}+8\\&=&-\dfrac{57750}{1273813}+\dfrac{1}{\dfrac{55}{4899}}+8\\&=&-\dfrac{57750}{1273813}+\dfrac{4899}{55}+8\\&=&\dfrac{6237233637}{70059715}+8\\&=&\dfrac{6797711357}{70059715}\\ \end{eqnarray*}