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 \[\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{62}{7}-\dfrac{49}{11}+\dfrac{\dfrac{\left(-\dfrac{103}{3}-\dfrac{83}{11}\right)+\dfrac{122}{11}-6-\dfrac{11}{7}\times\left(-\dfrac{83}{11}\right)\times\left(-\dfrac{83}{11}\right)\times\left(-7\right)}{12}}{-\dfrac{56}{5}-\dfrac{69}{8}+\dfrac{62}{7}-6-\dfrac{69}{8}+3-\dfrac{41}{3}-\dfrac{41}{3}}+\dfrac{\dfrac{\dfrac{-\dfrac{83}{11}}{\left(-\dfrac{61}{4}\right)\times\left(-3\right)\times\left(-\dfrac{62}{7}\right)\times\dfrac{31}{2}}}{12}}{-3}\times\left(-7\right)}}{12}\]

Cliquer ici pour afficher la solution

Exercice

On a $ X=\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{62}{7}-\dfrac{49}{11}+\dfrac{\dfrac{\left(-\dfrac{103}{3}-\dfrac{83}{11}\right)+\dfrac{122}{11}-6-\dfrac{11}{7}\times\left(-\dfrac{83}{11}\right)\times\left(-\dfrac{83}{11}\right)\times\left(-7\right)}{12}}{-\dfrac{56}{5}-\dfrac{69}{8}+\dfrac{62}{7}-6-\dfrac{69}{8}+3-\dfrac{41}{3}-\dfrac{41}{3}}+\dfrac{\dfrac{\dfrac{-\dfrac{83}{11}}{\left(-\dfrac{61}{4}\right)\times\left(-3\right)\times\left(-\dfrac{62}{7}\right)\times\dfrac{31}{2}}}{12}}{-3}\times\left(-7\right)}}{12}=\dfrac{84333353747643}{27618684569742924}$ . Voici le détail : \begin{eqnarray*} X &=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{62}{7}-\dfrac{49}{11}+\dfrac{\dfrac{-\dfrac{1382}{33}+\dfrac{122}{11}-6-\dfrac{11}{7}\times\left(-\dfrac{83}{11}\right)\times\left(-\dfrac{83}{11}\right)\times\left(-7\right)}{12}}{-\dfrac{56}{5}-\dfrac{69}{8}+\dfrac{62}{7}-6-\dfrac{69}{8}+3-\dfrac{41}{3}-\dfrac{41}{3}}+\dfrac{\dfrac{\dfrac{-\dfrac{83}{11}}{\left(-\dfrac{61}{4}\right)\times\left(-3\right)\times\left(-\dfrac{62}{7}\right)\times\dfrac{31}{2}}}{12}}{-3}\times\left(-7\right)}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{62}{7}-\dfrac{49}{11}+\dfrac{\dfrac{-\dfrac{1382}{33}+\dfrac{122}{11}-6-\left(-\dfrac{83}{7}\right)\times\left(-\dfrac{83}{11}\right)\times\left(-7\right)}{12}}{-\dfrac{56}{5}-\dfrac{69}{8}+\dfrac{62}{7}-6-\dfrac{69}{8}+3-\dfrac{41}{3}-\dfrac{41}{3}}+\dfrac{\dfrac{\dfrac{-\dfrac{83}{11}}{\left(-\dfrac{61}{4}\right)\times\left(-3\right)\times\left(-\dfrac{62}{7}\right)\times\dfrac{31}{2}}}{12}}{-3}\times\left(-7\right)}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{62}{7}-\dfrac{49}{11}+\dfrac{\dfrac{-\dfrac{1382}{33}+\dfrac{122}{11}-6-\dfrac{6889}{77}\times\left(-7\right)}{12}}{-\dfrac{56}{5}-\dfrac{69}{8}+\dfrac{62}{7}-6-\dfrac{69}{8}+3-\dfrac{41}{3}-\dfrac{41}{3}}+\dfrac{\dfrac{\dfrac{-\dfrac{83}{11}}{\left(-\dfrac{61}{4}\right)\times\left(-3\right)\times\left(-\dfrac{62}{7}\right)\times\dfrac{31}{2}}}{12}}{-3}\times\left(-7\right)}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{62}{7}-\dfrac{49}{11}+\dfrac{\dfrac{-\dfrac{1382}{33}+\dfrac{122}{11}-6+\dfrac{6889}{11}}{12}}{-\dfrac{56}{5}-\dfrac{69}{8}+\dfrac{62}{7}-6-\dfrac{69}{8}+3-\dfrac{41}{3}-\dfrac{41}{3}}+\dfrac{\dfrac{\dfrac{-\dfrac{83}{11}}{\left(-\dfrac{61}{4}\right)\times\left(-3\right)\times\left(-\dfrac{62}{7}\right)\times\dfrac{31}{2}}}{12}}{-3}\times\left(-7\right)}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{62}{7}-\dfrac{49}{11}+\dfrac{\dfrac{-\dfrac{1382}{33}+\dfrac{122}{11}-6+\dfrac{6889}{11}}{12}}{-\dfrac{56}{5}+\dfrac{13}{56}-6-\dfrac{69}{8}+3-\dfrac{41}{3}-\dfrac{41}{3}}+\dfrac{\dfrac{\dfrac{-\dfrac{83}{11}}{\left(-\dfrac{61}{4}\right)\times\left(-3\right)\times\left(-\dfrac{62}{7}\right)\times\dfrac{31}{2}}}{12}}{-3}\times\left(-7\right)}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{62}{7}-\dfrac{49}{11}+\dfrac{\dfrac{-\dfrac{1382}{33}+\dfrac{122}{11}-6+\dfrac{6889}{11}}{12}}{-\dfrac{56}{5}-\dfrac{323}{56}-\dfrac{69}{8}+3-\dfrac{41}{3}-\dfrac{41}{3}}+\dfrac{\dfrac{\dfrac{-\dfrac{83}{11}}{\left(-\dfrac{61}{4}\right)\times\left(-3\right)\times\left(-\dfrac{62}{7}\right)\times\dfrac{31}{2}}}{12}}{-3}\times\left(-7\right)}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{62}{7}-\dfrac{49}{11}+\dfrac{\dfrac{-\dfrac{1382}{33}+\dfrac{122}{11}-6+\dfrac{6889}{11}}{12}}{-\dfrac{56}{5}-\dfrac{323}{56}-\dfrac{69}{8}-\dfrac{32}{3}-\dfrac{41}{3}}+\dfrac{\dfrac{\dfrac{-\dfrac{83}{11}}{\left(-\dfrac{61}{4}\right)\times\left(-3\right)\times\left(-\dfrac{62}{7}\right)\times\dfrac{31}{2}}}{12}}{-3}\times\left(-7\right)}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{62}{7}-\dfrac{49}{11}+\dfrac{\dfrac{-\dfrac{1382}{33}+\dfrac{122}{11}-6+\dfrac{6889}{11}}{12}}{-\dfrac{56}{5}-\dfrac{323}{56}-\dfrac{69}{8}-\dfrac{73}{3}}+\dfrac{\dfrac{\dfrac{-\dfrac{83}{11}}{\left(-\dfrac{61}{4}\right)\times\left(-3\right)\times\left(-\dfrac{62}{7}\right)\times\dfrac{31}{2}}}{12}}{-3}\times\left(-7\right)}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{62}{7}-\dfrac{49}{11}+\dfrac{\dfrac{-\dfrac{1382}{33}+\dfrac{122}{11}-6+\dfrac{6889}{11}}{12}}{-\dfrac{56}{5}-\dfrac{323}{56}-\dfrac{69}{8}-\dfrac{73}{3}}+\dfrac{\dfrac{\dfrac{-\dfrac{83}{11}}{\dfrac{183}{4}\times\left(-\dfrac{62}{7}\right)\times\dfrac{31}{2}}}{12}}{-3}\times\left(-7\right)}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{62}{7}-\dfrac{49}{11}+\dfrac{\dfrac{-\dfrac{1382}{33}+\dfrac{122}{11}-6+\dfrac{6889}{11}}{12}}{-\dfrac{56}{5}-\dfrac{323}{56}-\dfrac{69}{8}-\dfrac{73}{3}}+\dfrac{\dfrac{\dfrac{-\dfrac{83}{11}}{\left(-\dfrac{5673}{14}\right)\times\dfrac{31}{2}}}{12}}{-3}\times\left(-7\right)}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{62}{7}-\dfrac{49}{11}+\dfrac{\dfrac{-\dfrac{1382}{33}+\dfrac{122}{11}-6+\dfrac{6889}{11}}{12}}{-\dfrac{56}{5}-\dfrac{323}{56}-\dfrac{69}{8}-\dfrac{73}{3}}+\dfrac{\dfrac{\dfrac{-\dfrac{83}{11}}{-\dfrac{175863}{28}}}{12}}{-3}\times\left(-7\right)}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{62}{7}-\dfrac{49}{11}+\dfrac{\dfrac{-\dfrac{1016}{33}-6+\dfrac{6889}{11}}{12}}{-\dfrac{56}{5}-\dfrac{323}{56}-\dfrac{69}{8}-\dfrac{73}{3}}+\dfrac{\dfrac{\dfrac{-\dfrac{83}{11}}{-\dfrac{175863}{28}}}{12}}{-3}\times\left(-7\right)}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{62}{7}-\dfrac{49}{11}+\dfrac{\dfrac{-\dfrac{1214}{33}+\dfrac{6889}{11}}{12}}{-\dfrac{56}{5}-\dfrac{323}{56}-\dfrac{69}{8}-\dfrac{73}{3}}+\dfrac{\dfrac{\dfrac{-\dfrac{83}{11}}{-\dfrac{175863}{28}}}{12}}{-3}\times\left(-7\right)}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{62}{7}-\dfrac{49}{11}+\dfrac{\dfrac{\dfrac{19453}{33}}{12}}{-\dfrac{56}{5}-\dfrac{323}{56}-\dfrac{69}{8}-\dfrac{73}{3}}+\dfrac{\dfrac{\dfrac{-\dfrac{83}{11}}{-\dfrac{175863}{28}}}{12}}{-3}\times\left(-7\right)}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{62}{7}-\dfrac{49}{11}+\dfrac{\dfrac{\dfrac{19453}{33}}{12}}{-\dfrac{4751}{280}-\dfrac{69}{8}-\dfrac{73}{3}}+\dfrac{\dfrac{\dfrac{-\dfrac{83}{11}}{-\dfrac{175863}{28}}}{12}}{-3}\times\left(-7\right)}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{62}{7}-\dfrac{49}{11}+\dfrac{\dfrac{\dfrac{19453}{33}}{12}}{-\dfrac{3583}{140}-\dfrac{73}{3}}+\dfrac{\dfrac{\dfrac{-\dfrac{83}{11}}{-\dfrac{175863}{28}}}{12}}{-3}\times\left(-7\right)}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{62}{7}-\dfrac{49}{11}+\dfrac{\dfrac{\dfrac{19453}{33}}{12}}{-\dfrac{20969}{420}}+\dfrac{\dfrac{\dfrac{-\dfrac{83}{11}}{-\dfrac{175863}{28}}}{12}}{-3}\times\left(-7\right)}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{62}{7}-\dfrac{49}{11}+\dfrac{\dfrac{\dfrac{19453}{33}}{12}}{-\dfrac{20969}{420}}+\dfrac{\dfrac{\dfrac{2324}{1934493}}{12}}{-3}\times\left(-7\right)}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{62}{7}-\dfrac{49}{11}+\dfrac{\dfrac{\dfrac{19453}{33}}{12}}{-\dfrac{20969}{420}}+\dfrac{\dfrac{581}{5803479}}{-3}\times\left(-7\right)}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{62}{7}-\dfrac{49}{11}+\dfrac{\dfrac{\dfrac{19453}{33}}{12}}{-\dfrac{20969}{420}}+\left(-\dfrac{581}{17410437}\right)\times\left(-7\right)}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{62}{7}-\dfrac{49}{11}+\dfrac{\dfrac{19453}{396}}{-\dfrac{20969}{420}}+\left(-\dfrac{581}{17410437}\right)\times\left(-7\right)}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{62}{7}-\dfrac{49}{11}-\dfrac{680855}{691977}+\left(-\dfrac{581}{17410437}\right)\times\left(-7\right)}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{62}{7}-\dfrac{49}{11}-\dfrac{680855}{691977}+\dfrac{4067}{17410437}}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{1025}{77}-\dfrac{680855}{691977}+\dfrac{4067}{17410437}}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{6295060}{440349}+\dfrac{4067}{17410437}}}{12}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{11}{7}}{-3}}{-\dfrac{109597954641837}{7666668522513}}}{12}\\&=&\dfrac{\dfrac{-\dfrac{11}{21}}{-\dfrac{109597954641837}{7666668522513}}}{12}\\&=&\dfrac{\dfrac{84333353747643}{2301557047478577}}{12}\\&=&\dfrac{84333353747643}{27618684569742924}\\ \end{eqnarray*}