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Exercice
Calculer \[\dfrac{\dfrac{\dfrac{\left(\dfrac{79}{6}-\dfrac{131}{10}+\dfrac{21}{5}-\left(-1\right)\times\left(-7\right)\right)-1-\dfrac{\dfrac{\dfrac{131}{10}\times\left(-\dfrac{55}{8}\right)}{\dfrac{8}{5}}}{-\dfrac{21}{5}}}{\dfrac{44}{3}}}{\dfrac{8}{5}}}{-1}-\dfrac{55}{8}+\dfrac{21}{5}+\dfrac{21}{5}+\dfrac{21}{5}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{\dfrac{\dfrac{\left(\dfrac{79}{6}-\dfrac{131}{10}+\dfrac{21}{5}-\left(-1\right)\times\left(-7\right)\right)-1-\dfrac{\dfrac{\dfrac{131}{10}\times\left(-\dfrac{55}{8}\right)}{\dfrac{8}{5}}}{-\dfrac{21}{5}}}{\dfrac{44}{3}}}{\dfrac{8}{5}}}{-1}-\dfrac{55}{8}+\dfrac{21}{5}+\dfrac{21}{5}+\dfrac{21}{5}=\dfrac{10179601}{1576960}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{\dfrac{\left(\dfrac{79}{6}-\dfrac{131}{10}+\dfrac{21}{5}-7\right)-1-\dfrac{\dfrac{\dfrac{131}{10}\times\left(-\dfrac{55}{8}\right)}{\dfrac{8}{5}}}{-\dfrac{21}{5}}}{\dfrac{44}{3}}}{\dfrac{8}{5}}}{-1}-\dfrac{55}{8}+\dfrac{21}{5}+\dfrac{21}{5}+\dfrac{21}{5}\\&=&\dfrac{\dfrac{\dfrac{\left(\dfrac{79}{6}-\dfrac{131}{10}+\dfrac{21}{5}-7\right)-1-\dfrac{\dfrac{-\dfrac{1441}{16}}{\dfrac{8}{5}}}{-\dfrac{21}{5}}}{\dfrac{44}{3}}}{\dfrac{8}{5}}}{-1}-\dfrac{55}{8}+\dfrac{21}{5}+\dfrac{21}{5}+\dfrac{21}{5}\\&=&\dfrac{\dfrac{\dfrac{\left(\dfrac{1}{15}+\dfrac{21}{5}-7\right)-1-\dfrac{\dfrac{-\dfrac{1441}{16}}{\dfrac{8}{5}}}{-\dfrac{21}{5}}}{\dfrac{44}{3}}}{\dfrac{8}{5}}}{-1}-\dfrac{55}{8}+\dfrac{21}{5}+\dfrac{21}{5}+\dfrac{21}{5}\\&=&\dfrac{\dfrac{\dfrac{\left(\dfrac{64}{15}-7\right)-1-\dfrac{\dfrac{-\dfrac{1441}{16}}{\dfrac{8}{5}}}{-\dfrac{21}{5}}}{\dfrac{44}{3}}}{\dfrac{8}{5}}}{-1}-\dfrac{55}{8}+\dfrac{21}{5}+\dfrac{21}{5}+\dfrac{21}{5}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{41}{15}-1-\dfrac{\dfrac{-\dfrac{1441}{16}}{\dfrac{8}{5}}}{-\dfrac{21}{5}}}{\dfrac{44}{3}}}{\dfrac{8}{5}}}{-1}-\dfrac{55}{8}+\dfrac{21}{5}+\dfrac{21}{5}+\dfrac{21}{5}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{41}{15}-1-\dfrac{-\dfrac{7205}{128}}{-\dfrac{21}{5}}}{\dfrac{44}{3}}}{\dfrac{8}{5}}}{-1}-\dfrac{55}{8}+\dfrac{21}{5}+\dfrac{21}{5}+\dfrac{21}{5}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{41}{15}-1-\dfrac{36025}{2688}}{\dfrac{44}{3}}}{\dfrac{8}{5}}}{-1}-\dfrac{55}{8}+\dfrac{21}{5}+\dfrac{21}{5}+\dfrac{21}{5}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{56}{15}-\dfrac{36025}{2688}}{\dfrac{44}{3}}}{\dfrac{8}{5}}}{-1}-\dfrac{55}{8}+\dfrac{21}{5}+\dfrac{21}{5}+\dfrac{21}{5}\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{76767}{4480}}{\dfrac{44}{3}}}{\dfrac{8}{5}}}{-1}-\dfrac{55}{8}+\dfrac{21}{5}+\dfrac{21}{5}+\dfrac{21}{5}\\&=&\dfrac{\dfrac{-\dfrac{230301}{197120}}{\dfrac{8}{5}}}{-1}-\dfrac{55}{8}+\dfrac{21}{5}+\dfrac{21}{5}+\dfrac{21}{5}\\&=&\dfrac{-\dfrac{230301}{315392}}{-1}-\dfrac{55}{8}+\dfrac{21}{5}+\dfrac{21}{5}+\dfrac{21}{5}\\&=&\dfrac{230301}{315392}-\dfrac{55}{8}+\dfrac{21}{5}+\dfrac{21}{5}+\dfrac{21}{5}\\&=&\dfrac{230301}{315392}-\dfrac{107}{40}+\dfrac{21}{5}+\dfrac{21}{5}\\&=&\dfrac{230301}{315392}+\dfrac{61}{40}+\dfrac{21}{5}\\&=&\dfrac{230301}{315392}+\dfrac{229}{40}\\&=&\dfrac{10179601}{1576960}\\
\end{eqnarray*}