L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[\dfrac{\dfrac{\left(-\dfrac{77}{9}\right)\times\left(-\dfrac{61}{2}\right)\times\dfrac{125}{8}}{\dfrac{117}{11}}}{-\dfrac{99}{7}}\times\left(-4-\dfrac{144}{7}+\dfrac{125}{8}-\dfrac{99}{7}-\dfrac{79}{5}\right)\times\left(-\dfrac{79}{5}-\dfrac{-\dfrac{14}{3}}{\dfrac{125}{8}}\right)+\dfrac{77}{9}+11+7-\dfrac{144}{7}\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=\dfrac{\dfrac{\left(-\dfrac{77}{9}\right)\times\left(-\dfrac{61}{2}\right)\times\dfrac{125}{8}}{\dfrac{117}{11}}}{-\dfrac{99}{7}}\times\left(-4-\dfrac{144}{7}+\dfrac{125}{8}-\dfrac{99}{7}-\dfrac{79}{5}\right)\times\left(-\dfrac{79}{5}-\dfrac{-\dfrac{14}{3}}{\dfrac{125}{8}}\right)+\dfrac{77}{9}+11+7-\dfrac{144}{7}=-\dfrac{16383187397453625}{1003045680000}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{\dfrac{4697}{18}\times\dfrac{125}{8}}{\dfrac{117}{11}}}{-\dfrac{99}{7}}\times\left(-4-\dfrac{144}{7}+\dfrac{125}{8}-\dfrac{99}{7}-\dfrac{79}{5}\right)\times\left(-\dfrac{79}{5}-\dfrac{-\dfrac{14}{3}}{\dfrac{125}{8}}\right)+\dfrac{77}{9}+11+7-\dfrac{144}{7}\\&=&\dfrac{\dfrac{\dfrac{587125}{144}}{\dfrac{117}{11}}}{-\dfrac{99}{7}}\times\left(-4-\dfrac{144}{7}+\dfrac{125}{8}-\dfrac{99}{7}-\dfrac{79}{5}\right)\times\left(-\dfrac{79}{5}-\dfrac{-\dfrac{14}{3}}{\dfrac{125}{8}}\right)+\dfrac{77}{9}+11+7-\dfrac{144}{7}\\&=&\dfrac{\dfrac{\dfrac{587125}{144}}{\dfrac{117}{11}}}{-\dfrac{99}{7}}\times\left(-\dfrac{172}{7}+\dfrac{125}{8}-\dfrac{99}{7}-\dfrac{79}{5}\right)\times\left(-\dfrac{79}{5}-\dfrac{-\dfrac{14}{3}}{\dfrac{125}{8}}\right)+\dfrac{77}{9}+11+7-\dfrac{144}{7}\\&=&\dfrac{\dfrac{\dfrac{587125}{144}}{\dfrac{117}{11}}}{-\dfrac{99}{7}}\times\left(-\dfrac{501}{56}-\dfrac{99}{7}-\dfrac{79}{5}\right)\times\left(-\dfrac{79}{5}-\dfrac{-\dfrac{14}{3}}{\dfrac{125}{8}}\right)+\dfrac{77}{9}+11+7-\dfrac{144}{7}\\&=&\dfrac{\dfrac{\dfrac{587125}{144}}{\dfrac{117}{11}}}{-\dfrac{99}{7}}\times\left(-\dfrac{501}{56}-\dfrac{99}{7}-\dfrac{79}{5}\right)\times\left(-\dfrac{79}{5}+\dfrac{112}{375}\right)+\dfrac{77}{9}+11+7-\dfrac{144}{7}\\&=&\dfrac{\dfrac{6458375}{16848}}{-\dfrac{99}{7}}\times\left(-\dfrac{501}{56}-\dfrac{99}{7}-\dfrac{79}{5}\right)\times\left(-\dfrac{79}{5}+\dfrac{112}{375}\right)+\dfrac{77}{9}+11+7-\dfrac{144}{7}\\&=&\left(-\dfrac{4109875}{151632}\right)\times\left(-\dfrac{501}{56}-\dfrac{99}{7}-\dfrac{79}{5}\right)\times\left(-\dfrac{79}{5}+\dfrac{112}{375}\right)+\dfrac{77}{9}+11+7-\dfrac{144}{7}\\&=&\left(-\dfrac{4109875}{151632}\right)\times\left(-\dfrac{1293}{56}-\dfrac{79}{5}\right)\times\left(-\dfrac{79}{5}+\dfrac{112}{375}\right)+\dfrac{77}{9}+11+7-\dfrac{144}{7}\\&=&\left(-\dfrac{4109875}{151632}\right)\times-\dfrac{10889}{280}\times\left(-\dfrac{79}{5}+\dfrac{112}{375}\right)+\dfrac{77}{9}+11+7-\dfrac{144}{7}\\&=&\left(-\dfrac{4109875}{151632}\right)\times-\dfrac{10889}{280}\times\left(-\dfrac{5813}{375}\right)+\dfrac{77}{9}+11+7-\dfrac{144}{7}\\&=&\left(\dfrac{44752428875}{42456960}\right)\times\left(-\dfrac{5813}{375}\right)+\dfrac{77}{9}+11+7-\dfrac{144}{7}\\&=&-\dfrac{260145869050375}{15921360000}+\dfrac{77}{9}+11+7-\dfrac{144}{7}\\&=&-\dfrac{2340086876733375}{143292240000}+11+7-\dfrac{144}{7}\\&=&-\dfrac{2338510662093375}{143292240000}+7-\dfrac{144}{7}\\&=&-\dfrac{2337507616413375}{143292240000}-\dfrac{144}{7}\\&=&-\dfrac{16383187397453625}{1003045680000}\\
\end{eqnarray*}