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Exercice
Calculer \[\dfrac{\dfrac{8-2\times7-8}{\dfrac{133}{12}}}{\dfrac{95}{8}}-\left(\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{34}{3}}{\dfrac{34}{3}}}{\dfrac{68}{3}}}{\dfrac{133}{12}+8\times\dfrac{68}{3}}}{\dfrac{34}{3}}+4-\dfrac{34}{3}\times\dfrac{\dfrac{68}{3}}{\dfrac{34}{3}}\times\left(-\dfrac{121}{3}\right)\right)-\left(-\dfrac{27}{7}-11\right)\]
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Exercice
On a \( X=\dfrac{\dfrac{8-2\times7-8}{\dfrac{133}{12}}}{\dfrac{95}{8}}-\left(\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{34}{3}}{\dfrac{34}{3}}}{\dfrac{68}{3}}}{\dfrac{133}{12}+8\times\dfrac{68}{3}}}{\dfrac{34}{3}}+4-\dfrac{34}{3}\times\dfrac{\dfrac{68}{3}}{\dfrac{34}{3}}\times\left(-\dfrac{121}{3}\right)\right)-\left(-\dfrac{27}{7}-11\right)=-\dfrac{137114685004417}{151764266430}\) . Voici le détail :
\begin{eqnarray*}
X &=&\dfrac{\dfrac{8-2\times7-8}{\dfrac{133}{12}}}{\dfrac{95}{8}}-\left(\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{34}{3}}{\dfrac{34}{3}}}{\dfrac{68}{3}}}{\dfrac{133}{12}+\dfrac{544}{3}}}{\dfrac{34}{3}}+4-\dfrac{34}{3}\times\dfrac{\dfrac{68}{3}}{\dfrac{34}{3}}\times\left(-\dfrac{121}{3}\right)\right)-\left(-\dfrac{27}{7}-11\right)\\&=&\dfrac{\dfrac{8-14-8}{\dfrac{133}{12}}}{\dfrac{95}{8}}-\left(\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{34}{3}}{\dfrac{34}{3}}}{\dfrac{68}{3}}}{\dfrac{133}{12}+\dfrac{544}{3}}}{\dfrac{34}{3}}+4-\dfrac{34}{3}\times\dfrac{\dfrac{68}{3}}{\dfrac{34}{3}}\times\left(-\dfrac{121}{3}\right)\right)-\left(-\dfrac{27}{7}-11\right)\\&=&\dfrac{\dfrac{8-14-8}{\dfrac{133}{12}}}{\dfrac{95}{8}}-\left(\dfrac{\dfrac{\dfrac{1}{\dfrac{68}{3}}}{\dfrac{133}{12}+\dfrac{544}{3}}}{\dfrac{34}{3}}+4-\dfrac{34}{3}\times\dfrac{\dfrac{68}{3}}{\dfrac{34}{3}}\times\left(-\dfrac{121}{3}\right)\right)-\left(-\dfrac{27}{7}-11\right)\\&=&\dfrac{\dfrac{8-14-8}{\dfrac{133}{12}}}{\dfrac{95}{8}}-\left(\dfrac{\dfrac{\dfrac{3}{68}}{\dfrac{133}{12}+\dfrac{544}{3}}}{\dfrac{34}{3}}+4-\dfrac{34}{3}\times\dfrac{\dfrac{68}{3}}{\dfrac{34}{3}}\times\left(-\dfrac{121}{3}\right)\right)-\left(-\dfrac{27}{7}-11\right)\\&=&\dfrac{\dfrac{8-14-8}{\dfrac{133}{12}}}{\dfrac{95}{8}}-\left(\dfrac{\dfrac{\dfrac{3}{68}}{\dfrac{2309}{12}}}{\dfrac{34}{3}}+4-\dfrac{34}{3}\times\dfrac{\dfrac{68}{3}}{\dfrac{34}{3}}\times\left(-\dfrac{121}{3}\right)\right)-\left(-\dfrac{27}{7}-11\right)\\&=&\dfrac{\dfrac{8-14-8}{\dfrac{133}{12}}}{\dfrac{95}{8}}-\left(\dfrac{\dfrac{\dfrac{3}{68}}{\dfrac{2309}{12}}}{\dfrac{34}{3}}+4-\dfrac{34}{3}\times2\times\left(-\dfrac{121}{3}\right)\right)-\left(-\dfrac{27}{7}-11\right)\\&=&\dfrac{\dfrac{-6-8}{\dfrac{133}{12}}}{\dfrac{95}{8}}-\left(\dfrac{\dfrac{\dfrac{3}{68}}{\dfrac{2309}{12}}}{\dfrac{34}{3}}+4-\dfrac{34}{3}\times2\times\left(-\dfrac{121}{3}\right)\right)-\left(-\dfrac{27}{7}-11\right)\\&=&\dfrac{\dfrac{-14}{\dfrac{133}{12}}}{\dfrac{95}{8}}-\left(\dfrac{\dfrac{\dfrac{3}{68}}{\dfrac{2309}{12}}}{\dfrac{34}{3}}+4-\dfrac{34}{3}\times2\times\left(-\dfrac{121}{3}\right)\right)-\left(-\dfrac{27}{7}-11\right)\\&=&\dfrac{\dfrac{-14}{\dfrac{133}{12}}}{\dfrac{95}{8}}-\left(\dfrac{\dfrac{9}{39253}}{\dfrac{34}{3}}+4-\dfrac{34}{3}\times2\times\left(-\dfrac{121}{3}\right)\right)-\left(-\dfrac{27}{7}-11\right)\\&=&\dfrac{\dfrac{-14}{\dfrac{133}{12}}}{\dfrac{95}{8}}-\left(\dfrac{27}{1334602}+4-\dfrac{34}{3}\times2\times\left(-\dfrac{121}{3}\right)\right)-\left(-\dfrac{27}{7}-11\right)\\&=&\dfrac{\dfrac{-14}{\dfrac{133}{12}}}{\dfrac{95}{8}}-\left(\dfrac{27}{1334602}+4-\dfrac{68}{3}\times\left(-\dfrac{121}{3}\right)\right)-\left(-\dfrac{27}{7}-11\right)\\&=&\dfrac{\dfrac{-14}{\dfrac{133}{12}}}{\dfrac{95}{8}}-\left(\dfrac{27}{1334602}+4+\dfrac{8228}{9}\right)-\left(-\dfrac{27}{7}-11\right)\\&=&\dfrac{-\dfrac{24}{19}}{\dfrac{95}{8}}-\left(\dfrac{27}{1334602}+4+\dfrac{8228}{9}\right)-\left(-\dfrac{27}{7}-11\right)\\&=&-\dfrac{192}{1805}-\left(\dfrac{27}{1334602}+4+\dfrac{8228}{9}\right)-\left(-\dfrac{27}{7}-11\right)\\&=&-\dfrac{192}{1805}-\left(\dfrac{5338435}{1334602}+\dfrac{8228}{9}\right)-\left(-\dfrac{27}{7}-11\right)\\&=&-\dfrac{192}{1805}-\dfrac{11029151171}{12011418}-\left(-\dfrac{27}{7}-11\right)\\&=&-\dfrac{192}{1805}-\dfrac{11029151171}{12011418}+\dfrac{104}{7}\\&=&-\dfrac{19909924055911}{21680609490}+\dfrac{104}{7}\\&=&-\dfrac{137114685004417}{151764266430}\\
\end{eqnarray*}