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Exercice
Calculer \[\dfrac{\dfrac{\dfrac{-\dfrac{61}{4}}{-\dfrac{11}{2}}}{\dfrac{59}{2}+\dfrac{89}{11}}}{\dfrac{89}{11}\times\dfrac{\dfrac{\left(-3\right)\times\left(-\dfrac{61}{4}\right)\times9}{-\dfrac{123}{10}}}{3-9-9-3}}+9+\dfrac{-\dfrac{11}{2}}{3-\dfrac{23}{4}}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{\dfrac{\dfrac{-\dfrac{61}{4}}{-\dfrac{11}{2}}}{\dfrac{59}{2}+\dfrac{89}{11}}}{\dfrac{89}{11}\times\dfrac{\dfrac{\left(-3\right)\times\left(-\dfrac{61}{4}\right)\times9}{-\dfrac{123}{10}}}{3-9-9-3}}+9+\dfrac{-\dfrac{11}{2}}{3-\dfrac{23}{4}}=\dfrac{4049969}{368015}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{\dfrac{-\dfrac{61}{4}}{-\dfrac{11}{2}}}{\dfrac{59}{2}+\dfrac{89}{11}}}{\dfrac{89}{11}\times\dfrac{\dfrac{\dfrac{183}{4}\times9}{-\dfrac{123}{10}}}{3-9-9-3}}+9+\dfrac{-\dfrac{11}{2}}{3-\dfrac{23}{4}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{61}{4}}{-\dfrac{11}{2}}}{\dfrac{59}{2}+\dfrac{89}{11}}}{\dfrac{89}{11}\times\dfrac{\dfrac{\dfrac{1647}{4}}{-\dfrac{123}{10}}}{3-9-9-3}}+9+\dfrac{-\dfrac{11}{2}}{3-\dfrac{23}{4}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{61}{4}}{-\dfrac{11}{2}}}{\dfrac{59}{2}+\dfrac{89}{11}}}{\dfrac{89}{11}\times\dfrac{\dfrac{\dfrac{1647}{4}}{-\dfrac{123}{10}}}{-6-9-3}}+9+\dfrac{-\dfrac{11}{2}}{3-\dfrac{23}{4}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{61}{4}}{-\dfrac{11}{2}}}{\dfrac{59}{2}+\dfrac{89}{11}}}{\dfrac{89}{11}\times\dfrac{\dfrac{\dfrac{1647}{4}}{-\dfrac{123}{10}}}{-15-3}}+9+\dfrac{-\dfrac{11}{2}}{3-\dfrac{23}{4}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{61}{4}}{-\dfrac{11}{2}}}{\dfrac{59}{2}+\dfrac{89}{11}}}{\dfrac{89}{11}\times\dfrac{\dfrac{\dfrac{1647}{4}}{-\dfrac{123}{10}}}{-18}}+9+\dfrac{-\dfrac{11}{2}}{3-\dfrac{23}{4}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{61}{4}}{-\dfrac{11}{2}}}{\dfrac{59}{2}+\dfrac{89}{11}}}{\dfrac{89}{11}\times\dfrac{-\dfrac{2745}{82}}{-18}}+9+\dfrac{-\dfrac{11}{2}}{3-\dfrac{23}{4}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{61}{4}}{-\dfrac{11}{2}}}{\dfrac{59}{2}+\dfrac{89}{11}}}{\dfrac{89}{11}\times\dfrac{305}{164}}+9+\dfrac{-\dfrac{11}{2}}{3-\dfrac{23}{4}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{61}{4}}{-\dfrac{11}{2}}}{\dfrac{827}{22}}}{\dfrac{89}{11}\times\dfrac{305}{164}}+9+\dfrac{-\dfrac{11}{2}}{3-\dfrac{23}{4}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{61}{4}}{-\dfrac{11}{2}}}{\dfrac{827}{22}}}{\dfrac{27145}{1804}}+9+\dfrac{-\dfrac{11}{2}}{3-\dfrac{23}{4}}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{61}{4}}{-\dfrac{11}{2}}}{\dfrac{827}{22}}}{\dfrac{27145}{1804}}+9+\dfrac{-\dfrac{11}{2}}{-\dfrac{11}{4}}\\&=&\dfrac{\dfrac{\dfrac{61}{22}}{\dfrac{827}{22}}}{\dfrac{27145}{1804}}+9+\dfrac{-\dfrac{11}{2}}{-\dfrac{11}{4}}\\&=&\dfrac{\dfrac{61}{827}}{\dfrac{27145}{1804}}+9+\dfrac{-\dfrac{11}{2}}{-\dfrac{11}{4}}\\&=&\dfrac{1804}{368015}+9+\dfrac{-\dfrac{11}{2}}{-\dfrac{11}{4}}\\&=&\dfrac{1804}{368015}+9+2\\&=&\dfrac{3313939}{368015}+2\\&=&\dfrac{4049969}{368015}\\
\end{eqnarray*}