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Exercice
Calculer \[-\dfrac{53}{4}+\left(-\dfrac{53}{4}\right)\times\dfrac{\dfrac{129}{2}}{-\dfrac{131}{10}}\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{83}{4}}{11}}{\dfrac{107}{3}}}{\dfrac{129}{2}}}{\dfrac{107}{3}-11-\dfrac{48}{7}}}{\dfrac{4}{3}-11-7}}{-12}\times\left(-\dfrac{53}{4}+\dfrac{29}{6}+11+\dfrac{129}{2}\right)\times\dfrac{48}{7}\]
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Exercice
On a \( X=-\dfrac{53}{4}+\left(-\dfrac{53}{4}\right)\times\dfrac{\dfrac{129}{2}}{-\dfrac{131}{10}}\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{83}{4}}{11}}{\dfrac{107}{3}}}{\dfrac{129}{2}}}{\dfrac{107}{3}-11-\dfrac{48}{7}}}{\dfrac{4}{3}-11-7}}{-12}\times\left(-\dfrac{53}{4}+\dfrac{29}{6}+11+\dfrac{129}{2}\right)\times\dfrac{48}{7}=-\dfrac{53016443353540800}{3999155866675200}\) . Voici le détail :
\begin{eqnarray*}
X &=&-\dfrac{53}{4}+\left(-\dfrac{53}{4}\right)\times\dfrac{\dfrac{129}{2}}{-\dfrac{131}{10}}\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{83}{44}}{\dfrac{107}{3}}}{\dfrac{129}{2}}}{\dfrac{107}{3}-11-\dfrac{48}{7}}}{\dfrac{4}{3}-11-7}}{-12}\times\left(-\dfrac{53}{4}+\dfrac{29}{6}+11+\dfrac{129}{2}\right)\times\dfrac{48}{7}\\&=&-\dfrac{53}{4}+\left(-\dfrac{53}{4}\right)\times\dfrac{\dfrac{129}{2}}{-\dfrac{131}{10}}\times\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{249}{4708}}{\dfrac{129}{2}}}{\dfrac{107}{3}-11-\dfrac{48}{7}}}{\dfrac{4}{3}-11-7}}{-12}\times\left(-\dfrac{53}{4}+\dfrac{29}{6}+11+\dfrac{129}{2}\right)\times\dfrac{48}{7}\\&=&-\dfrac{53}{4}+\left(-\dfrac{53}{4}\right)\times\dfrac{\dfrac{129}{2}}{-\dfrac{131}{10}}\times\dfrac{\dfrac{\dfrac{-\dfrac{83}{101222}}{\dfrac{107}{3}-11-\dfrac{48}{7}}}{\dfrac{4}{3}-11-7}}{-12}\times\left(-\dfrac{53}{4}+\dfrac{29}{6}+11+\dfrac{129}{2}\right)\times\dfrac{48}{7}\\&=&-\dfrac{53}{4}+\left(-\dfrac{53}{4}\right)\times\dfrac{\dfrac{129}{2}}{-\dfrac{131}{10}}\times\dfrac{\dfrac{\dfrac{-\dfrac{83}{101222}}{\dfrac{74}{3}-\dfrac{48}{7}}}{\dfrac{4}{3}-11-7}}{-12}\times\left(-\dfrac{53}{4}+\dfrac{29}{6}+11+\dfrac{129}{2}\right)\times\dfrac{48}{7}\\&=&-\dfrac{53}{4}+\left(-\dfrac{53}{4}\right)\times\dfrac{\dfrac{129}{2}}{-\dfrac{131}{10}}\times\dfrac{\dfrac{\dfrac{-\dfrac{83}{101222}}{\dfrac{374}{21}}}{\dfrac{4}{3}-11-7}}{-12}\times\left(-\dfrac{53}{4}+\dfrac{29}{6}+11+\dfrac{129}{2}\right)\times\dfrac{48}{7}\\&=&-\dfrac{53}{4}+\left(-\dfrac{53}{4}\right)\times\dfrac{\dfrac{129}{2}}{-\dfrac{131}{10}}\times\dfrac{\dfrac{\dfrac{-\dfrac{83}{101222}}{\dfrac{374}{21}}}{-\dfrac{29}{3}-7}}{-12}\times\left(-\dfrac{53}{4}+\dfrac{29}{6}+11+\dfrac{129}{2}\right)\times\dfrac{48}{7}\\&=&-\dfrac{53}{4}+\left(-\dfrac{53}{4}\right)\times\dfrac{\dfrac{129}{2}}{-\dfrac{131}{10}}\times\dfrac{\dfrac{\dfrac{-\dfrac{83}{101222}}{\dfrac{374}{21}}}{-\dfrac{50}{3}}}{-12}\times\left(-\dfrac{53}{4}+\dfrac{29}{6}+11+\dfrac{129}{2}\right)\times\dfrac{48}{7}\\&=&-\dfrac{53}{4}+\left(-\dfrac{53}{4}\right)\times\left(-\dfrac{645}{131}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{83}{101222}}{\dfrac{374}{21}}}{-\dfrac{50}{3}}}{-12}\times\left(-\dfrac{53}{4}+\dfrac{29}{6}+11+\dfrac{129}{2}\right)\times\dfrac{48}{7}\\&=&-\dfrac{53}{4}+\left(-\dfrac{53}{4}\right)\times\left(-\dfrac{645}{131}\right)\times\dfrac{\dfrac{-\dfrac{1743}{37857028}}{-\dfrac{50}{3}}}{-12}\times\left(-\dfrac{53}{4}+\dfrac{29}{6}+11+\dfrac{129}{2}\right)\times\dfrac{48}{7}\\&=&-\dfrac{53}{4}+\left(-\dfrac{53}{4}\right)\times\left(-\dfrac{645}{131}\right)\times\dfrac{\dfrac{5229}{1892851400}}{-12}\times\left(-\dfrac{53}{4}+\dfrac{29}{6}+11+\dfrac{129}{2}\right)\times\dfrac{48}{7}\\&=&-\dfrac{53}{4}+\left(-\dfrac{53}{4}\right)\times\left(-\dfrac{645}{131}\right)\times-\dfrac{5229}{22714216800}\times\left(-\dfrac{53}{4}+\dfrac{29}{6}+11+\dfrac{129}{2}\right)\times\dfrac{48}{7}\\&=&-\dfrac{53}{4}+\left(-\dfrac{53}{4}\right)\times\left(-\dfrac{645}{131}\right)\times-\dfrac{5229}{22714216800}\times\left(-\dfrac{101}{12}+11+\dfrac{129}{2}\right)\times\dfrac{48}{7}\\&=&-\dfrac{53}{4}+\left(-\dfrac{53}{4}\right)\times\left(-\dfrac{645}{131}\right)\times-\dfrac{5229}{22714216800}\times\left(\dfrac{31}{12}+\dfrac{129}{2}\right)\times\dfrac{48}{7}\\&=&-\dfrac{53}{4}+\left(-\dfrac{53}{4}\right)\times\left(-\dfrac{645}{131}\right)\times-\dfrac{5229}{22714216800}\times\dfrac{805}{12}\times\dfrac{48}{7}\\&=&-\dfrac{53}{4}+\left(-\dfrac{53}{4}\right)\times\left(\dfrac{3372705}{2975562400800}\right)\times\dfrac{805}{12}\times\dfrac{48}{7}\\&=&-\dfrac{53}{4}+\left(-\dfrac{53}{4}\right)\times\left(\dfrac{2715027525}{35706748809600}\right)\times\dfrac{48}{7}\\&=&-\dfrac{53}{4}+\left(-\dfrac{53}{4}\right)\times\left(\dfrac{130321321200}{249947241667200}\right)\\&=&-\dfrac{53}{4}-\dfrac{6907030023600}{999788966668800}\\&=&-\dfrac{53016443353540800}{3999155866675200}\\
\end{eqnarray*}