Ataraxy

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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 \[\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{2}{3}}{\dfrac{29}{2}}}{\dfrac{29}{2}}\times\left(10+8+12\right)\times8}{\left(10\times1\times\left(-3\right)+\dfrac{113}{4}+\dfrac{113}{4}\right)-\dfrac{\dfrac{-\dfrac{17}{3}+9}{-\dfrac{113}{4}+10}}{8}}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{\dfrac{-12+\dfrac{29}{2}+4}{12\times1-1-\dfrac{-\dfrac{113}{4}}{4}}}{12}\]

Cliquer ici pour afficher la solution

Exercice

On a $ X=\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{2}{3}}{\dfrac{29}{2}}}{\dfrac{29}{2}}\times\left(10+8+12\right)\times8}{\left(10\times1\times\left(-3\right)+\dfrac{113}{4}+\dfrac{113}{4}\right)-\dfrac{\dfrac{-\dfrac{17}{3}+9}{-\dfrac{113}{4}+10}}{8}}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{\dfrac{-12+\dfrac{29}{2}+4}{12\times1-1-\dfrac{-\dfrac{113}{4}}{4}}}{12}=\dfrac{101412244186}{8470500699}$ . Voici le détail : \begin{eqnarray*} X &=&\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{2}{3}}{\dfrac{29}{2}}}{\dfrac{29}{2}}\times\left(10+8+12\right)\times8}{\left(10\times\left(-3\right)+\dfrac{113}{4}+\dfrac{113}{4}\right)-\dfrac{\dfrac{-\dfrac{17}{3}+9}{-\dfrac{113}{4}+10}}{8}}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{\dfrac{-12+\dfrac{29}{2}+4}{12\times1-1-\dfrac{-\dfrac{113}{4}}{4}}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{2}{3}}{\dfrac{29}{2}}}{\dfrac{29}{2}}\times\left(10+8+12\right)\times8}{\left(-30+\dfrac{113}{4}+\dfrac{113}{4}\right)-\dfrac{\dfrac{-\dfrac{17}{3}+9}{-\dfrac{113}{4}+10}}{8}}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{\dfrac{-12+\dfrac{29}{2}+4}{12\times1-1-\dfrac{-\dfrac{113}{4}}{4}}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{2}{3}}{\dfrac{29}{2}}}{\dfrac{29}{2}}\times\left(10+8+12\right)\times8}{\left(-30+\dfrac{113}{4}+\dfrac{113}{4}\right)-\dfrac{\dfrac{\dfrac{10}{3}}{-\dfrac{113}{4}+10}}{8}}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{\dfrac{-12+\dfrac{29}{2}+4}{12\times1-1-\dfrac{-\dfrac{113}{4}}{4}}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{2}{3}}{\dfrac{29}{2}}}{\dfrac{29}{2}}\times\left(10+8+12\right)\times8}{\left(-30+\dfrac{113}{4}+\dfrac{113}{4}\right)-\dfrac{\dfrac{\dfrac{10}{3}}{-\dfrac{73}{4}}}{8}}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{\dfrac{-12+\dfrac{29}{2}+4}{12\times1-1-\dfrac{-\dfrac{113}{4}}{4}}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{2}{3}}{\dfrac{29}{2}}}{\dfrac{29}{2}}\times\left(10+8+12\right)\times8}{\left(-30+\dfrac{113}{4}+\dfrac{113}{4}\right)-\dfrac{\dfrac{\dfrac{10}{3}}{-\dfrac{73}{4}}}{8}}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{\dfrac{-12+\dfrac{29}{2}+4}{12-1-\dfrac{-\dfrac{113}{4}}{4}}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{2}{3}}{\dfrac{29}{2}}}{\dfrac{29}{2}}\times\left(10+8+12\right)\times8}{\left(-30+\dfrac{113}{4}+\dfrac{113}{4}\right)-\dfrac{\dfrac{\dfrac{10}{3}}{-\dfrac{73}{4}}}{8}}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{\dfrac{-12+\dfrac{29}{2}+4}{12-1+\dfrac{113}{16}}}{12}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{4}{87}}{\dfrac{29}{2}}\times\left(10+8+12\right)\times8}{\left(-30+\dfrac{113}{4}+\dfrac{113}{4}\right)-\dfrac{\dfrac{\dfrac{10}{3}}{-\dfrac{73}{4}}}{8}}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{\dfrac{-12+\dfrac{29}{2}+4}{12-1+\dfrac{113}{16}}}{12}\\&=&\dfrac{\dfrac{\left(-\dfrac{8}{2523}\right)\times\left(10+8+12\right)\times8}{\left(-30+\dfrac{113}{4}+\dfrac{113}{4}\right)-\dfrac{\dfrac{\dfrac{10}{3}}{-\dfrac{73}{4}}}{8}}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{\dfrac{-12+\dfrac{29}{2}+4}{12-1+\dfrac{113}{16}}}{12}\\&=&\dfrac{\dfrac{\left(-\dfrac{8}{2523}\right)\times\left(18+12\right)\times8}{\left(-30+\dfrac{113}{4}+\dfrac{113}{4}\right)-\dfrac{\dfrac{\dfrac{10}{3}}{-\dfrac{73}{4}}}{8}}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{\dfrac{-12+\dfrac{29}{2}+4}{12-1+\dfrac{113}{16}}}{12}\\&=&\dfrac{\dfrac{\left(-\dfrac{8}{2523}\right)\times30\times8}{\left(-30+\dfrac{113}{4}+\dfrac{113}{4}\right)-\dfrac{\dfrac{\dfrac{10}{3}}{-\dfrac{73}{4}}}{8}}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{\dfrac{-12+\dfrac{29}{2}+4}{12-1+\dfrac{113}{16}}}{12}\\&=&\dfrac{\dfrac{\left(-\dfrac{8}{2523}\right)\times30\times8}{\left(-\dfrac{7}{4}+\dfrac{113}{4}\right)-\dfrac{\dfrac{\dfrac{10}{3}}{-\dfrac{73}{4}}}{8}}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{\dfrac{-12+\dfrac{29}{2}+4}{12-1+\dfrac{113}{16}}}{12}\\&=&\dfrac{\dfrac{\left(-\dfrac{8}{2523}\right)\times30\times8}{\dfrac{53}{2}-\dfrac{\dfrac{\dfrac{10}{3}}{-\dfrac{73}{4}}}{8}}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{\dfrac{-12+\dfrac{29}{2}+4}{12-1+\dfrac{113}{16}}}{12}\\&=&\dfrac{\dfrac{\left(-\dfrac{8}{2523}\right)\times30\times8}{\dfrac{53}{2}-\dfrac{-\dfrac{40}{219}}{8}}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{\dfrac{-12+\dfrac{29}{2}+4}{12-1+\dfrac{113}{16}}}{12}\\&=&\dfrac{\dfrac{\left(-\dfrac{8}{2523}\right)\times30\times8}{\dfrac{53}{2}+\dfrac{5}{219}}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{\dfrac{-12+\dfrac{29}{2}+4}{12-1+\dfrac{113}{16}}}{12}\\&=&\dfrac{\dfrac{\left(-\dfrac{8}{2523}\right)\times30\times8}{\dfrac{53}{2}+\dfrac{5}{219}}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{\dfrac{\dfrac{5}{2}+4}{12-1+\dfrac{113}{16}}}{12}\\&=&\dfrac{\dfrac{\left(-\dfrac{8}{2523}\right)\times30\times8}{\dfrac{53}{2}+\dfrac{5}{219}}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{\dfrac{\dfrac{13}{2}}{12-1+\dfrac{113}{16}}}{12}\\&=&\dfrac{\dfrac{\left(-\dfrac{8}{2523}\right)\times30\times8}{\dfrac{53}{2}+\dfrac{5}{219}}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{\dfrac{\dfrac{13}{2}}{11+\dfrac{113}{16}}}{12}\\&=&\dfrac{\dfrac{\left(-\dfrac{8}{2523}\right)\times30\times8}{\dfrac{53}{2}+\dfrac{5}{219}}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{\dfrac{\dfrac{13}{2}}{\dfrac{289}{16}}}{12}\\&=&\dfrac{\dfrac{\left(-\dfrac{80}{841}\right)\times8}{\dfrac{53}{2}+\dfrac{5}{219}}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{\dfrac{\dfrac{13}{2}}{\dfrac{289}{16}}}{12}\\&=&\dfrac{\dfrac{-\dfrac{640}{841}}{\dfrac{53}{2}+\dfrac{5}{219}}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{\dfrac{\dfrac{13}{2}}{\dfrac{289}{16}}}{12}\\&=&\dfrac{\dfrac{-\dfrac{640}{841}}{\dfrac{11617}{438}}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{\dfrac{\dfrac{13}{2}}{\dfrac{289}{16}}}{12}\\&=&\dfrac{\dfrac{-\dfrac{640}{841}}{\dfrac{11617}{438}}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{\dfrac{104}{289}}{12}\\&=&\dfrac{\dfrac{-\dfrac{640}{841}}{\dfrac{11617}{438}}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{26}{867}\\&=&\dfrac{-\dfrac{280320}{9769897}}{-12}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{26}{867}\\&=&\dfrac{23360}{9769897}+12-\dfrac{17}{3}+\dfrac{17}{3}-\dfrac{26}{867}\\&=&\dfrac{23360}{9769897}+12+0-\dfrac{26}{867}\\&=&\dfrac{23360}{9769897}+12-\dfrac{26}{867}\\&=&\dfrac{117262124}{9769897}-\dfrac{26}{867}\\&=&\dfrac{101412244186}{8470500699}\\ \end{eqnarray*}