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Exercice
Calculer \[\left(-11\right)\times\dfrac{\dfrac{\dfrac{135}{11}-\dfrac{47}{8}\times\left(-11\right)\times\dfrac{131}{12}+\dfrac{131}{12}+\dfrac{-11}{-11}+0+6}{\dfrac{131}{12}+9-9+9}}{4}\times\left(4\times\dfrac{131}{12}\times\dfrac{\dfrac{-11}{\dfrac{131}{12}}}{3}-\left(\dfrac{47}{8}+\dfrac{135}{11}+\dfrac{\dfrac{29}{3}}{-\dfrac{57}{2}}\right)\right)\]
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Exercice
On a \( X=\left(-11\right)\times\dfrac{\dfrac{\dfrac{135}{11}-\dfrac{47}{8}\times\left(-11\right)\times\dfrac{131}{12}+\dfrac{131}{12}+\dfrac{-11}{-11}+0+6}{\dfrac{131}{12}+9-9+9}}{4}\times\left(4\times\dfrac{131}{12}\times\dfrac{\dfrac{-11}{\dfrac{131}{12}}}{3}-\left(\dfrac{47}{8}+\dfrac{135}{11}+\dfrac{\dfrac{29}{3}}{-\dfrac{57}{2}}\right)\right)=\dfrac{379649690499}{115087104}\) . Voici le détail :
\begin{eqnarray*}
X &=&\left(-11\right)\times\dfrac{\dfrac{\dfrac{135}{11}-\left(-\dfrac{517}{8}\right)\times\dfrac{131}{12}+\dfrac{131}{12}+\dfrac{-11}{-11}+0+6}{\dfrac{131}{12}+9-9+9}}{4}\times\left(4\times\dfrac{131}{12}\times\dfrac{\dfrac{-11}{\dfrac{131}{12}}}{3}-\left(\dfrac{47}{8}+\dfrac{135}{11}+\dfrac{\dfrac{29}{3}}{-\dfrac{57}{2}}\right)\right)\\&=&\left(-11\right)\times\dfrac{\dfrac{\dfrac{135}{11}+\dfrac{67727}{96}+\dfrac{131}{12}+\dfrac{-11}{-11}+0+6}{\dfrac{131}{12}+9-9+9}}{4}\times\left(4\times\dfrac{131}{12}\times\dfrac{\dfrac{-11}{\dfrac{131}{12}}}{3}-\left(\dfrac{47}{8}+\dfrac{135}{11}+\dfrac{\dfrac{29}{3}}{-\dfrac{57}{2}}\right)\right)\\&=&\left(-11\right)\times\dfrac{\dfrac{\dfrac{135}{11}+\dfrac{67727}{96}+\dfrac{131}{12}+1+0+6}{\dfrac{131}{12}+9-9+9}}{4}\times\left(4\times\dfrac{131}{12}\times\dfrac{\dfrac{-11}{\dfrac{131}{12}}}{3}-\left(\dfrac{47}{8}+\dfrac{135}{11}+\dfrac{\dfrac{29}{3}}{-\dfrac{57}{2}}\right)\right)\\&=&\left(-11\right)\times\dfrac{\dfrac{\dfrac{757957}{1056}+\dfrac{131}{12}+1+0+6}{\dfrac{131}{12}+9-9+9}}{4}\times\left(4\times\dfrac{131}{12}\times\dfrac{\dfrac{-11}{\dfrac{131}{12}}}{3}-\left(\dfrac{47}{8}+\dfrac{135}{11}+\dfrac{\dfrac{29}{3}}{-\dfrac{57}{2}}\right)\right)\\&=&\left(-11\right)\times\dfrac{\dfrac{\dfrac{757957}{1056}+\dfrac{131}{12}+1+6}{\dfrac{131}{12}+9-9+9}}{4}\times\left(4\times\dfrac{131}{12}\times\dfrac{\dfrac{-11}{\dfrac{131}{12}}}{3}-\left(\dfrac{47}{8}+\dfrac{135}{11}+\dfrac{\dfrac{29}{3}}{-\dfrac{57}{2}}\right)\right)\\&=&\left(-11\right)\times\dfrac{\dfrac{\dfrac{757957}{1056}+\dfrac{131}{12}+7}{\dfrac{131}{12}+9-9+9}}{4}\times\left(4\times\dfrac{131}{12}\times\dfrac{\dfrac{-11}{\dfrac{131}{12}}}{3}-\left(\dfrac{47}{8}+\dfrac{135}{11}+\dfrac{\dfrac{29}{3}}{-\dfrac{57}{2}}\right)\right)\\&=&\left(-11\right)\times\dfrac{\dfrac{\dfrac{757957}{1056}+\dfrac{131}{12}+7}{\dfrac{131}{12}+0+9}}{4}\times\left(4\times\dfrac{131}{12}\times\dfrac{\dfrac{-11}{\dfrac{131}{12}}}{3}-\left(\dfrac{47}{8}+\dfrac{135}{11}+\dfrac{\dfrac{29}{3}}{-\dfrac{57}{2}}\right)\right)\\&=&\left(-11\right)\times\dfrac{\dfrac{\dfrac{757957}{1056}+\dfrac{131}{12}+7}{\dfrac{131}{12}+0+9}}{4}\times\left(4\times\dfrac{131}{12}\times\dfrac{-\dfrac{132}{131}}{3}-\left(\dfrac{47}{8}+\dfrac{135}{11}+\dfrac{\dfrac{29}{3}}{-\dfrac{57}{2}}\right)\right)\\&=&\left(-11\right)\times\dfrac{\dfrac{\dfrac{757957}{1056}+\dfrac{131}{12}+7}{\dfrac{131}{12}+0+9}}{4}\times\left(4\times\dfrac{131}{12}\times\left(-\dfrac{44}{131}\right)-\left(\dfrac{47}{8}+\dfrac{135}{11}+\dfrac{\dfrac{29}{3}}{-\dfrac{57}{2}}\right)\right)\\&=&\left(-11\right)\times\dfrac{\dfrac{\dfrac{757957}{1056}+\dfrac{131}{12}+7}{\dfrac{131}{12}+0+9}}{4}\times\left(4\times\dfrac{131}{12}\times\left(-\dfrac{44}{131}\right)-\left(\dfrac{47}{8}+\dfrac{135}{11}-\dfrac{58}{171}\right)\right)\\&=&\left(-11\right)\times\dfrac{\dfrac{\dfrac{256495}{352}+7}{\dfrac{131}{12}+0+9}}{4}\times\left(4\times\dfrac{131}{12}\times\left(-\dfrac{44}{131}\right)-\left(\dfrac{47}{8}+\dfrac{135}{11}-\dfrac{58}{171}\right)\right)\\&=&\left(-11\right)\times\dfrac{\dfrac{\dfrac{258959}{352}}{\dfrac{131}{12}+0+9}}{4}\times\left(4\times\dfrac{131}{12}\times\left(-\dfrac{44}{131}\right)-\left(\dfrac{47}{8}+\dfrac{135}{11}-\dfrac{58}{171}\right)\right)\\&=&\left(-11\right)\times\dfrac{\dfrac{\dfrac{258959}{352}}{\dfrac{131}{12}+9}}{4}\times\left(4\times\dfrac{131}{12}\times\left(-\dfrac{44}{131}\right)-\left(\dfrac{47}{8}+\dfrac{135}{11}-\dfrac{58}{171}\right)\right)\\&=&\left(-11\right)\times\dfrac{\dfrac{\dfrac{258959}{352}}{\dfrac{239}{12}}}{4}\times\left(4\times\dfrac{131}{12}\times\left(-\dfrac{44}{131}\right)-\left(\dfrac{47}{8}+\dfrac{135}{11}-\dfrac{58}{171}\right)\right)\\&=&\left(-11\right)\times\dfrac{\dfrac{\dfrac{258959}{352}}{\dfrac{239}{12}}}{4}\times\left(\dfrac{131}{3}\times\left(-\dfrac{44}{131}\right)-\left(\dfrac{47}{8}+\dfrac{135}{11}-\dfrac{58}{171}\right)\right)\\&=&\left(-11\right)\times\dfrac{\dfrac{\dfrac{258959}{352}}{\dfrac{239}{12}}}{4}\times\left(-\dfrac{44}{3}-\left(\dfrac{47}{8}+\dfrac{135}{11}-\dfrac{58}{171}\right)\right)\\&=&\left(-11\right)\times\dfrac{\dfrac{\dfrac{258959}{352}}{\dfrac{239}{12}}}{4}\times\left(-\dfrac{44}{3}-\left(\dfrac{1597}{88}-\dfrac{58}{171}\right)\right)\\&=&\left(-11\right)\times\dfrac{\dfrac{\dfrac{258959}{352}}{\dfrac{239}{12}}}{4}\times\left(-\dfrac{44}{3}-\dfrac{267983}{15048}\right)\\&=&\left(-11\right)\times\dfrac{\dfrac{776877}{21032}}{4}\times\left(-\dfrac{44}{3}-\dfrac{267983}{15048}\right)\\&=&\left(-11\right)\times\dfrac{776877}{84128}\times\left(-\dfrac{44}{3}-\dfrac{267983}{15048}\right)\\&=&\left(-11\right)\times\dfrac{776877}{84128}\times\left(-\dfrac{488687}{15048}\right)\\&=&\left(-\dfrac{776877}{7648}\right)\times\left(-\dfrac{488687}{15048}\right)\\&=&\dfrac{379649690499}{115087104}\\
\end{eqnarray*}