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Exercice
Calculer \[\dfrac{\dfrac{\left(\dfrac{39}{2}+\dfrac{\dfrac{\dfrac{44}{5}}{-\dfrac{128}{9}-\dfrac{3}{8}+9}}{-\dfrac{3}{8}}\right)\times\left(-\dfrac{3}{8}-\left(6+\dfrac{21}{2}\right)\right)}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{6}{\dfrac{17}{6}}}{\dfrac{-\dfrac{21}{2}}{-\dfrac{107}{5}}-6+8}}{4}}{3}}{3}}}{-\dfrac{128}{9}}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{\dfrac{\left(\dfrac{39}{2}+\dfrac{\dfrac{\dfrac{44}{5}}{-\dfrac{128}{9}-\dfrac{3}{8}+9}}{-\dfrac{3}{8}}\right)\times\left(-\dfrac{3}{8}-\left(6+\dfrac{21}{2}\right)\right)}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{6}{\dfrac{17}{6}}}{\dfrac{-\dfrac{21}{2}}{-\dfrac{107}{5}}-6+8}}{4}}{3}}{3}}}{-\dfrac{128}{9}}=\dfrac{210232261863}{176623616}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{\left(\dfrac{39}{2}+\dfrac{\dfrac{\dfrac{44}{5}}{-\dfrac{1051}{72}+9}}{-\dfrac{3}{8}}\right)\times\left(-\dfrac{3}{8}-\left(6+\dfrac{21}{2}\right)\right)}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{6}{\dfrac{17}{6}}}{\dfrac{-\dfrac{21}{2}}{-\dfrac{107}{5}}-6+8}}{4}}{3}}{3}}}{-\dfrac{128}{9}}\\&=&\dfrac{\dfrac{\left(\dfrac{39}{2}+\dfrac{\dfrac{\dfrac{44}{5}}{-\dfrac{403}{72}}}{-\dfrac{3}{8}}\right)\times\left(-\dfrac{3}{8}-\left(6+\dfrac{21}{2}\right)\right)}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{6}{\dfrac{17}{6}}}{\dfrac{-\dfrac{21}{2}}{-\dfrac{107}{5}}-6+8}}{4}}{3}}{3}}}{-\dfrac{128}{9}}\\&=&\dfrac{\dfrac{\left(\dfrac{39}{2}+\dfrac{\dfrac{\dfrac{44}{5}}{-\dfrac{403}{72}}}{-\dfrac{3}{8}}\right)\times\left(-\dfrac{3}{8}-\left(6+\dfrac{21}{2}\right)\right)}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{6}{\dfrac{17}{6}}}{\dfrac{105}{214}-6+8}}{4}}{3}}{3}}}{-\dfrac{128}{9}}\\&=&\dfrac{\dfrac{\left(\dfrac{39}{2}+\dfrac{-\dfrac{3168}{2015}}{-\dfrac{3}{8}}\right)\times\left(-\dfrac{3}{8}-\left(6+\dfrac{21}{2}\right)\right)}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{6}{\dfrac{17}{6}}}{\dfrac{105}{214}-6+8}}{4}}{3}}{3}}}{-\dfrac{128}{9}}\\&=&\dfrac{\dfrac{\left(\dfrac{39}{2}+\dfrac{8448}{2015}\right)\times\left(-\dfrac{3}{8}-\left(6+\dfrac{21}{2}\right)\right)}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{6}{\dfrac{17}{6}}}{\dfrac{105}{214}-6+8}}{4}}{3}}{3}}}{-\dfrac{128}{9}}\\&=&\dfrac{\dfrac{\left(\dfrac{39}{2}+\dfrac{8448}{2015}\right)\times\left(-\dfrac{3}{8}-\dfrac{33}{2}\right)}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{6}{\dfrac{17}{6}}}{\dfrac{105}{214}-6+8}}{4}}{3}}{3}}}{-\dfrac{128}{9}}\\&=&\dfrac{\dfrac{\left(\dfrac{39}{2}+\dfrac{8448}{2015}\right)\times\left(-\dfrac{3}{8}-\dfrac{33}{2}\right)}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{6}{\dfrac{17}{6}}}{-\dfrac{1179}{214}+8}}{4}}{3}}{3}}}{-\dfrac{128}{9}}\\&=&\dfrac{\dfrac{\left(\dfrac{39}{2}+\dfrac{8448}{2015}\right)\times\left(-\dfrac{3}{8}-\dfrac{33}{2}\right)}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{6}{\dfrac{17}{6}}}{\dfrac{533}{214}}}{4}}{3}}{3}}}{-\dfrac{128}{9}}\\&=&\dfrac{\dfrac{\dfrac{95481}{4030}\times\left(-\dfrac{3}{8}-\dfrac{33}{2}\right)}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{6}{\dfrac{17}{6}}}{\dfrac{533}{214}}}{4}}{3}}{3}}}{-\dfrac{128}{9}}\\&=&\dfrac{\dfrac{\dfrac{95481}{4030}\times\left(-\dfrac{135}{8}\right)}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{6}{\dfrac{17}{6}}}{\dfrac{533}{214}}}{4}}{3}}{3}}}{-\dfrac{128}{9}}\\&=&\dfrac{\dfrac{\dfrac{95481}{4030}\times\left(-\dfrac{135}{8}\right)}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{36}{17}}{\dfrac{533}{214}}}{4}}{3}}{3}}}{-\dfrac{128}{9}}\\&=&\dfrac{\dfrac{\dfrac{95481}{4030}\times\left(-\dfrac{135}{8}\right)}{\dfrac{\dfrac{\dfrac{\dfrac{7704}{9061}}{4}}{3}}{3}}}{-\dfrac{128}{9}}\\&=&\dfrac{\dfrac{-\dfrac{2577987}{6448}}{\dfrac{\dfrac{\dfrac{\dfrac{7704}{9061}}{4}}{3}}{3}}}{-\dfrac{128}{9}}\\&=&\dfrac{\dfrac{-\dfrac{2577987}{6448}}{\dfrac{\dfrac{\dfrac{1926}{9061}}{3}}{3}}}{-\dfrac{128}{9}}\\&=&\dfrac{\dfrac{-\dfrac{2577987}{6448}}{\dfrac{\dfrac{642}{9061}}{3}}}{-\dfrac{128}{9}}\\&=&\dfrac{\dfrac{-\dfrac{2577987}{6448}}{\dfrac{214}{9061}}}{-\dfrac{128}{9}}\\&=&\dfrac{-\dfrac{23359140207}{1379872}}{-\dfrac{128}{9}}\\&=&\dfrac{210232261863}{176623616}\\
\end{eqnarray*}