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Exercice

L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
Si vous regénérez la page (F5) les valeurs seront changées.
La correction se trouve en bas de page.

Exercice


Calculer \[\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{21}{5}-\left(\dfrac{46}{11}-\left(\dfrac{15}{8}+\dfrac{125}{2}-\dfrac{25}{6}+\dfrac{37}{5}\right)\right)}{-\dfrac{20}{3}}}{-\dfrac{20}{3}+\left(-3\right)\times\dfrac{15}{8}-4+\dfrac{25}{6}-\dfrac{21}{5}}}{\dfrac{\dfrac{\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{37}{5}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{15}{8}}{-\dfrac{20}{3}}}{1}}{10}\times1\times\left(\dfrac{25}{6}+\dfrac{37}{5}\right)}{\left(-4\right)\times1\times\left(-3\right)\times1\times\dfrac{25}{6}\times\left(-\dfrac{125}{2}\right)\times\dfrac{55}{6}\times1-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{21}{5}-\left(\dfrac{46}{11}-\left(\dfrac{15}{8}+\dfrac{125}{2}-\dfrac{25}{6}+\dfrac{37}{5}\right)\right)}{-\dfrac{20}{3}}}{-\dfrac{20}{3}+\left(-3\right)\times\dfrac{15}{8}-4+\dfrac{25}{6}-\dfrac{21}{5}}}{\dfrac{\dfrac{\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{37}{5}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{15}{8}}{-\dfrac{20}{3}}}{1}}{10}\times1\times\left(\dfrac{25}{6}+\dfrac{37}{5}\right)}{\left(-4\right)\times1\times\left(-3\right)\times1\times\dfrac{25}{6}\times\left(-\dfrac{125}{2}\right)\times\dfrac{55}{6}\times1-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}=-\dfrac{2.0687217709485E+20}{321055719840662400}\) . Voici le détail : \begin{eqnarray*} X &=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{21}{5}-\left(\dfrac{46}{11}-\left(\dfrac{515}{8}-\dfrac{25}{6}+\dfrac{37}{5}\right)\right)}{-\dfrac{20}{3}}}{-\dfrac{20}{3}+\left(-3\right)\times\dfrac{15}{8}-4+\dfrac{25}{6}-\dfrac{21}{5}}}{\dfrac{\dfrac{\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{37}{5}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{15}{8}}{-\dfrac{20}{3}}}{1}}{10}\times1\times\left(\dfrac{25}{6}+\dfrac{37}{5}\right)}{\left(-4\right)\times1\times\left(-3\right)\times1\times\dfrac{25}{6}\times\left(-\dfrac{125}{2}\right)\times\dfrac{55}{6}\times1-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{21}{5}-\left(\dfrac{46}{11}-\left(\dfrac{1445}{24}+\dfrac{37}{5}\right)\right)}{-\dfrac{20}{3}}}{-\dfrac{20}{3}+\left(-3\right)\times\dfrac{15}{8}-4+\dfrac{25}{6}-\dfrac{21}{5}}}{\dfrac{\dfrac{\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{37}{5}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{15}{8}}{-\dfrac{20}{3}}}{1}}{10}\times1\times\left(\dfrac{25}{6}+\dfrac{37}{5}\right)}{\left(-4\right)\times1\times\left(-3\right)\times1\times\dfrac{25}{6}\times\left(-\dfrac{125}{2}\right)\times\dfrac{55}{6}\times1-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{21}{5}-\left(\dfrac{46}{11}-\dfrac{8113}{120}\right)}{-\dfrac{20}{3}}}{-\dfrac{20}{3}+\left(-3\right)\times\dfrac{15}{8}-4+\dfrac{25}{6}-\dfrac{21}{5}}}{\dfrac{\dfrac{\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{37}{5}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{15}{8}}{-\dfrac{20}{3}}}{1}}{10}\times1\times\left(\dfrac{25}{6}+\dfrac{37}{5}\right)}{\left(-4\right)\times1\times\left(-3\right)\times1\times\dfrac{25}{6}\times\left(-\dfrac{125}{2}\right)\times\dfrac{55}{6}\times1-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{21}{5}-\left(\dfrac{46}{11}-\dfrac{8113}{120}\right)}{-\dfrac{20}{3}}}{-\dfrac{20}{3}-\dfrac{45}{8}-4+\dfrac{25}{6}-\dfrac{21}{5}}}{\dfrac{\dfrac{\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{37}{5}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{15}{8}}{-\dfrac{20}{3}}}{1}}{10}\times1\times\left(\dfrac{25}{6}+\dfrac{37}{5}\right)}{\left(-4\right)\times1\times\left(-3\right)\times1\times\dfrac{25}{6}\times\left(-\dfrac{125}{2}\right)\times\dfrac{55}{6}\times1-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{21}{5}-\left(\dfrac{46}{11}-\dfrac{8113}{120}\right)}{-\dfrac{20}{3}}}{-\dfrac{20}{3}-\dfrac{45}{8}-4+\dfrac{25}{6}-\dfrac{21}{5}}}{\dfrac{\dfrac{\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{37}{5}\right)\times\dfrac{\dfrac{-\dfrac{9}{32}}{1}}{10}\times1\times\left(\dfrac{25}{6}+\dfrac{37}{5}\right)}{\left(-4\right)\times1\times\left(-3\right)\times1\times\dfrac{25}{6}\times\left(-\dfrac{125}{2}\right)\times\dfrac{55}{6}\times1-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{21}{5}-\left(\dfrac{46}{11}-\dfrac{8113}{120}\right)}{-\dfrac{20}{3}}}{-\dfrac{20}{3}-\dfrac{45}{8}-4+\dfrac{25}{6}-\dfrac{21}{5}}}{\dfrac{\dfrac{\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{37}{5}\right)\times\dfrac{-\dfrac{9}{32}}{10}\times1\times\left(\dfrac{25}{6}+\dfrac{37}{5}\right)}{\left(-4\right)\times1\times\left(-3\right)\times1\times\dfrac{25}{6}\times\left(-\dfrac{125}{2}\right)\times\dfrac{55}{6}\times1-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{21}{5}-\left(\dfrac{46}{11}-\dfrac{8113}{120}\right)}{-\dfrac{20}{3}}}{-\dfrac{20}{3}-\dfrac{45}{8}-4+\dfrac{25}{6}-\dfrac{21}{5}}}{\dfrac{\dfrac{\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{9}{320}\right)\times1\times\left(\dfrac{25}{6}+\dfrac{37}{5}\right)}{\left(-4\right)\times1\times\left(-3\right)\times1\times\dfrac{25}{6}\times\left(-\dfrac{125}{2}\right)\times\dfrac{55}{6}\times1-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{21}{5}-\left(\dfrac{46}{11}-\dfrac{8113}{120}\right)}{-\dfrac{20}{3}}}{-\dfrac{20}{3}-\dfrac{45}{8}-4+\dfrac{25}{6}-\dfrac{21}{5}}}{\dfrac{\dfrac{\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{9}{320}\right)\times1\times\left(\dfrac{25}{6}+\dfrac{37}{5}\right)}{\left(-4\right)\times\left(-3\right)\times1\times\dfrac{25}{6}\times\left(-\dfrac{125}{2}\right)\times\dfrac{55}{6}\times1-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{21}{5}-\left(\dfrac{46}{11}-\dfrac{8113}{120}\right)}{-\dfrac{20}{3}}}{-\dfrac{20}{3}-\dfrac{45}{8}-4+\dfrac{25}{6}-\dfrac{21}{5}}}{\dfrac{\dfrac{\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{9}{320}\right)\times1\times\left(\dfrac{25}{6}+\dfrac{37}{5}\right)}{12\times1\times\dfrac{25}{6}\times\left(-\dfrac{125}{2}\right)\times\dfrac{55}{6}\times1-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{21}{5}-\left(\dfrac{46}{11}-\dfrac{8113}{120}\right)}{-\dfrac{20}{3}}}{-\dfrac{20}{3}-\dfrac{45}{8}-4+\dfrac{25}{6}-\dfrac{21}{5}}}{\dfrac{\dfrac{\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{9}{320}\right)\times1\times\left(\dfrac{25}{6}+\dfrac{37}{5}\right)}{12\times\dfrac{25}{6}\times\left(-\dfrac{125}{2}\right)\times\dfrac{55}{6}\times1-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{21}{5}-\left(\dfrac{46}{11}-\dfrac{8113}{120}\right)}{-\dfrac{20}{3}}}{-\dfrac{20}{3}-\dfrac{45}{8}-4+\dfrac{25}{6}-\dfrac{21}{5}}}{\dfrac{\dfrac{\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{9}{320}\right)\times1\times\left(\dfrac{25}{6}+\dfrac{37}{5}\right)}{12\times\left(-\dfrac{3125}{12}\right)\times\dfrac{55}{6}\times1-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{21}{5}-\left(\dfrac{46}{11}-\dfrac{8113}{120}\right)}{-\dfrac{20}{3}}}{-\dfrac{20}{3}-\dfrac{45}{8}-4+\dfrac{25}{6}-\dfrac{21}{5}}}{\dfrac{\dfrac{\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{9}{320}\right)\times1\times\left(\dfrac{25}{6}+\dfrac{37}{5}\right)}{12\times\left(-\dfrac{171875}{72}\right)\times1-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{21}{5}-\left(\dfrac{46}{11}-\dfrac{8113}{120}\right)}{-\dfrac{20}{3}}}{-\dfrac{20}{3}-\dfrac{45}{8}-4+\dfrac{25}{6}-\dfrac{21}{5}}}{\dfrac{\dfrac{\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{9}{320}\right)\times1\times\left(\dfrac{25}{6}+\dfrac{37}{5}\right)}{12\times\left(-\dfrac{171875}{72}\right)-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{21}{5}+\dfrac{83723}{1320}}{-\dfrac{20}{3}}}{-\dfrac{20}{3}-\dfrac{45}{8}-4+\dfrac{25}{6}-\dfrac{21}{5}}}{\dfrac{\dfrac{\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{9}{320}\right)\times1\times\left(\dfrac{25}{6}+\dfrac{37}{5}\right)}{12\times\left(-\dfrac{171875}{72}\right)-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{21}{5}+\dfrac{83723}{1320}}{-\dfrac{20}{3}}}{-\dfrac{295}{24}-4+\dfrac{25}{6}-\dfrac{21}{5}}}{\dfrac{\dfrac{\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{9}{320}\right)\times1\times\left(\dfrac{25}{6}+\dfrac{37}{5}\right)}{12\times\left(-\dfrac{171875}{72}\right)-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{21}{5}+\dfrac{83723}{1320}}{-\dfrac{20}{3}}}{-\dfrac{391}{24}+\dfrac{25}{6}-\dfrac{21}{5}}}{\dfrac{\dfrac{\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{9}{320}\right)\times1\times\left(\dfrac{25}{6}+\dfrac{37}{5}\right)}{12\times\left(-\dfrac{171875}{72}\right)-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{21}{5}+\dfrac{83723}{1320}}{-\dfrac{20}{3}}}{-\dfrac{97}{8}-\dfrac{21}{5}}}{\dfrac{\dfrac{\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{37}{5}\right)\times\left(-\dfrac{9}{320}\right)\times1\times\left(\dfrac{25}{6}+\dfrac{37}{5}\right)}{12\times\left(-\dfrac{171875}{72}\right)-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{21}{5}+\dfrac{83723}{1320}}{-\dfrac{20}{3}}}{-\dfrac{97}{8}-\dfrac{21}{5}}}{\dfrac{\dfrac{\left(-\dfrac{37}{5}\right)\times\dfrac{333}{1600}\times1\times\left(\dfrac{25}{6}+\dfrac{37}{5}\right)}{12\times\left(-\dfrac{171875}{72}\right)-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{21}{5}+\dfrac{83723}{1320}}{-\dfrac{20}{3}}}{-\dfrac{97}{8}-\dfrac{21}{5}}}{\dfrac{\dfrac{\left(-\dfrac{37}{5}\right)\times\dfrac{333}{1600}\times\left(\dfrac{25}{6}+\dfrac{37}{5}\right)}{12\times\left(-\dfrac{171875}{72}\right)-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{21}{5}+\dfrac{83723}{1320}}{-\dfrac{20}{3}}}{-\dfrac{97}{8}-\dfrac{21}{5}}}{\dfrac{\dfrac{\left(-\dfrac{37}{5}\right)\times\dfrac{333}{1600}\times\dfrac{347}{30}}{12\times\left(-\dfrac{171875}{72}\right)-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{21}{5}+\dfrac{83723}{1320}}{-\dfrac{20}{3}}}{-\dfrac{97}{8}-\dfrac{21}{5}}}{\dfrac{\dfrac{\left(-\dfrac{37}{5}\right)\times\dfrac{333}{1600}\times\dfrac{347}{30}}{-\dfrac{171875}{6}-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{78179}{1320}}{-\dfrac{20}{3}}}{-\dfrac{97}{8}-\dfrac{21}{5}}}{\dfrac{\dfrac{\left(-\dfrac{37}{5}\right)\times\dfrac{333}{1600}\times\dfrac{347}{30}}{-\dfrac{171875}{6}-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{78179}{1320}}{-\dfrac{20}{3}}}{-\dfrac{653}{40}}}{\dfrac{\dfrac{\left(-\dfrac{37}{5}\right)\times\dfrac{333}{1600}\times\dfrac{347}{30}}{-\dfrac{171875}{6}-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{78179}{1320}}{-\dfrac{20}{3}}}{-\dfrac{653}{40}}}{\dfrac{\dfrac{\left(-\dfrac{12321}{8000}\right)\times\dfrac{347}{30}}{-\dfrac{171875}{6}-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{78179}{1320}}{-\dfrac{20}{3}}}{-\dfrac{653}{40}}}{\dfrac{\dfrac{-\dfrac{1425129}{80000}}{-\dfrac{171875}{6}-\dfrac{46}{11}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{78179}{1320}}{-\dfrac{20}{3}}}{-\dfrac{653}{40}}}{\dfrac{\dfrac{-\dfrac{1425129}{80000}}{-\dfrac{1890901}{66}-\dfrac{46}{11}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{78179}{1320}}{-\dfrac{20}{3}}}{-\dfrac{653}{40}}}{\dfrac{\dfrac{-\dfrac{1425129}{80000}}{-\dfrac{1891177}{66}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{78179}{8800}}{-\dfrac{653}{40}}}{\dfrac{\dfrac{-\dfrac{1425129}{80000}}{-\dfrac{1891177}{66}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{78179}{143660}}{\dfrac{\dfrac{-\dfrac{1425129}{80000}}{-\dfrac{1891177}{66}}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{78179}{143660}}{\dfrac{\dfrac{94058514}{151294160000}}{-\dfrac{53}{8}}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{78179}{143660}}{-\dfrac{752468112}{8018590480000}}}{\dfrac{55}{6}}}{\dfrac{46}{11}-\dfrac{21}{5}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{78179}{143660}}{-\dfrac{752468112}{8018590480000}}}{\dfrac{55}{6}}}{-\dfrac{1}{55}+1}\\&=&\dfrac{\dfrac{\dfrac{\dfrac{78179}{143660}}{-\dfrac{752468112}{8018590480000}}}{\dfrac{55}{6}}}{\dfrac{54}{55}}\\&=&\dfrac{\dfrac{-\dfrac{626885385135920000}{108099568969920}}{\dfrac{55}{6}}}{\dfrac{54}{55}}\\&=&\dfrac{-\dfrac{3761312310815520000}{5945476293345600}}{\dfrac{54}{55}}\\&=&-\dfrac{2.0687217709485E+20}{321055719840662400}\\ \end{eqnarray*}