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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 \[\left(\left(\left(\dfrac{83}{6}+4\times\dfrac{123}{8}+\dfrac{19}{2}\right)-\left(-\dfrac{95}{7}\right)\times\dfrac{83}{6}\right)-\dfrac{\dfrac{\dfrac{110}{7}}{-11}}{\dfrac{\dfrac{123}{8}\times8\times\dfrac{23}{5}}{-5+\dfrac{19}{2}+8}}-\left(\left(-\dfrac{17}{4}-9+3\right)-\dfrac{\dfrac{123}{8}}{-\dfrac{118}{9}}\right)\times\dfrac{\dfrac{110}{7}}{-\dfrac{17}{4}}\times\dfrac{\dfrac{3}{\dfrac{71}{8}}}{-\dfrac{118}{9}}\times\left(\dfrac{110}{7}+\dfrac{95}{7}+\dfrac{118}{9}\right)\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\left(\dfrac{123}{8}-9\right)-\left(-11-\dfrac{116}{7}\times\dfrac{123}{8}\times\left(-11\right)+\dfrac{17}{4}\right)}\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=\left(\left(\left(\dfrac{83}{6}+4\times\dfrac{123}{8}+\dfrac{19}{2}\right)-\left(-\dfrac{95}{7}\right)\times\dfrac{83}{6}\right)-\dfrac{\dfrac{\dfrac{110}{7}}{-11}}{\dfrac{\dfrac{123}{8}\times8\times\dfrac{23}{5}}{-5+\dfrac{19}{2}+8}}-\left(\left(-\dfrac{17}{4}-9+3\right)-\dfrac{\dfrac{123}{8}}{-\dfrac{118}{9}}\right)\times\dfrac{\dfrac{110}{7}}{-\dfrac{17}{4}}\times\dfrac{\dfrac{3}{\dfrac{71}{8}}}{-\dfrac{118}{9}}\times\left(\dfrac{110}{7}+\dfrac{95}{7}+\dfrac{118}{9}\right)\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\left(\dfrac{123}{8}-9\right)-\left(-11-\dfrac{116}{7}\times\dfrac{123}{8}\times\left(-11\right)+\dfrac{17}{4}\right)}=\dfrac{2.1262152439522E+22}{6.6801316060301E+19}\) . Voici le détail : \begin{eqnarray*} X &=&\left(\left(\left(\dfrac{83}{6}+\dfrac{123}{2}+\dfrac{19}{2}\right)-\left(-\dfrac{95}{7}\right)\times\dfrac{83}{6}\right)-\dfrac{\dfrac{\dfrac{110}{7}}{-11}}{\dfrac{\dfrac{123}{8}\times8\times\dfrac{23}{5}}{-5+\dfrac{19}{2}+8}}-\left(\left(-\dfrac{17}{4}-9+3\right)-\dfrac{\dfrac{123}{8}}{-\dfrac{118}{9}}\right)\times\dfrac{\dfrac{110}{7}}{-\dfrac{17}{4}}\times\dfrac{\dfrac{3}{\dfrac{71}{8}}}{-\dfrac{118}{9}}\times\left(\dfrac{110}{7}+\dfrac{95}{7}+\dfrac{118}{9}\right)\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\left(\dfrac{123}{8}-9\right)-\left(-11-\dfrac{116}{7}\times\dfrac{123}{8}\times\left(-11\right)+\dfrac{17}{4}\right)}\\&=&\left(\left(\left(\dfrac{83}{6}+\dfrac{123}{2}+\dfrac{19}{2}\right)-\left(-\dfrac{95}{7}\right)\times\dfrac{83}{6}\right)-\dfrac{\dfrac{\dfrac{110}{7}}{-11}}{\dfrac{123\times\dfrac{23}{5}}{-5+\dfrac{19}{2}+8}}-\left(\left(-\dfrac{17}{4}-9+3\right)-\dfrac{\dfrac{123}{8}}{-\dfrac{118}{9}}\right)\times\dfrac{\dfrac{110}{7}}{-\dfrac{17}{4}}\times\dfrac{\dfrac{3}{\dfrac{71}{8}}}{-\dfrac{118}{9}}\times\left(\dfrac{110}{7}+\dfrac{95}{7}+\dfrac{118}{9}\right)\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\left(\dfrac{123}{8}-9\right)-\left(-11-\dfrac{116}{7}\times\dfrac{123}{8}\times\left(-11\right)+\dfrac{17}{4}\right)}\\&=&\left(\left(\left(\dfrac{83}{6}+\dfrac{123}{2}+\dfrac{19}{2}\right)-\left(-\dfrac{95}{7}\right)\times\dfrac{83}{6}\right)-\dfrac{\dfrac{\dfrac{110}{7}}{-11}}{\dfrac{\dfrac{2829}{5}}{-5+\dfrac{19}{2}+8}}-\left(\left(-\dfrac{17}{4}-9+3\right)-\dfrac{\dfrac{123}{8}}{-\dfrac{118}{9}}\right)\times\dfrac{\dfrac{110}{7}}{-\dfrac{17}{4}}\times\dfrac{\dfrac{3}{\dfrac{71}{8}}}{-\dfrac{118}{9}}\times\left(\dfrac{110}{7}+\dfrac{95}{7}+\dfrac{118}{9}\right)\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\left(\dfrac{123}{8}-9\right)-\left(-11-\dfrac{116}{7}\times\dfrac{123}{8}\times\left(-11\right)+\dfrac{17}{4}\right)}\\&=&\left(\left(\left(\dfrac{83}{6}+\dfrac{123}{2}+\dfrac{19}{2}\right)-\left(-\dfrac{95}{7}\right)\times\dfrac{83}{6}\right)-\dfrac{\dfrac{\dfrac{110}{7}}{-11}}{\dfrac{\dfrac{2829}{5}}{\dfrac{9}{2}+8}}-\left(\left(-\dfrac{17}{4}-9+3\right)-\dfrac{\dfrac{123}{8}}{-\dfrac{118}{9}}\right)\times\dfrac{\dfrac{110}{7}}{-\dfrac{17}{4}}\times\dfrac{\dfrac{3}{\dfrac{71}{8}}}{-\dfrac{118}{9}}\times\left(\dfrac{110}{7}+\dfrac{95}{7}+\dfrac{118}{9}\right)\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\left(\dfrac{123}{8}-9\right)-\left(-11-\dfrac{116}{7}\times\dfrac{123}{8}\times\left(-11\right)+\dfrac{17}{4}\right)}\\&=&\left(\left(\left(\dfrac{83}{6}+\dfrac{123}{2}+\dfrac{19}{2}\right)-\left(-\dfrac{95}{7}\right)\times\dfrac{83}{6}\right)-\dfrac{\dfrac{\dfrac{110}{7}}{-11}}{\dfrac{\dfrac{2829}{5}}{\dfrac{25}{2}}}-\left(\left(-\dfrac{17}{4}-9+3\right)-\dfrac{\dfrac{123}{8}}{-\dfrac{118}{9}}\right)\times\dfrac{\dfrac{110}{7}}{-\dfrac{17}{4}}\times\dfrac{\dfrac{3}{\dfrac{71}{8}}}{-\dfrac{118}{9}}\times\left(\dfrac{110}{7}+\dfrac{95}{7}+\dfrac{118}{9}\right)\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\left(\dfrac{123}{8}-9\right)-\left(-11-\dfrac{116}{7}\times\dfrac{123}{8}\times\left(-11\right)+\dfrac{17}{4}\right)}\\&=&\left(\left(\left(\dfrac{83}{6}+\dfrac{123}{2}+\dfrac{19}{2}\right)-\left(-\dfrac{95}{7}\right)\times\dfrac{83}{6}\right)-\dfrac{\dfrac{\dfrac{110}{7}}{-11}}{\dfrac{\dfrac{2829}{5}}{\dfrac{25}{2}}}-\left(\left(-\dfrac{53}{4}+3\right)-\dfrac{\dfrac{123}{8}}{-\dfrac{118}{9}}\right)\times\dfrac{\dfrac{110}{7}}{-\dfrac{17}{4}}\times\dfrac{\dfrac{3}{\dfrac{71}{8}}}{-\dfrac{118}{9}}\times\left(\dfrac{110}{7}+\dfrac{95}{7}+\dfrac{118}{9}\right)\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\left(\dfrac{123}{8}-9\right)-\left(-11-\dfrac{116}{7}\times\dfrac{123}{8}\times\left(-11\right)+\dfrac{17}{4}\right)}\\&=&\left(\left(\left(\dfrac{83}{6}+\dfrac{123}{2}+\dfrac{19}{2}\right)-\left(-\dfrac{95}{7}\right)\times\dfrac{83}{6}\right)-\dfrac{\dfrac{\dfrac{110}{7}}{-11}}{\dfrac{\dfrac{2829}{5}}{\dfrac{25}{2}}}-\left(-\dfrac{41}{4}-\dfrac{\dfrac{123}{8}}{-\dfrac{118}{9}}\right)\times\dfrac{\dfrac{110}{7}}{-\dfrac{17}{4}}\times\dfrac{\dfrac{3}{\dfrac{71}{8}}}{-\dfrac{118}{9}}\times\left(\dfrac{110}{7}+\dfrac{95}{7}+\dfrac{118}{9}\right)\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\left(\dfrac{123}{8}-9\right)-\left(-11-\dfrac{116}{7}\times\dfrac{123}{8}\times\left(-11\right)+\dfrac{17}{4}\right)}\\&=&\left(\left(\left(\dfrac{83}{6}+\dfrac{123}{2}+\dfrac{19}{2}\right)-\left(-\dfrac{95}{7}\right)\times\dfrac{83}{6}\right)-\dfrac{\dfrac{\dfrac{110}{7}}{-11}}{\dfrac{\dfrac{2829}{5}}{\dfrac{25}{2}}}-\left(-\dfrac{41}{4}+\dfrac{1107}{944}\right)\times\dfrac{\dfrac{110}{7}}{-\dfrac{17}{4}}\times\dfrac{\dfrac{3}{\dfrac{71}{8}}}{-\dfrac{118}{9}}\times\left(\dfrac{110}{7}+\dfrac{95}{7}+\dfrac{118}{9}\right)\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\left(\dfrac{123}{8}-9\right)-\left(-11-\dfrac{116}{7}\times\dfrac{123}{8}\times\left(-11\right)+\dfrac{17}{4}\right)}\\&=&\left(\left(\left(\dfrac{83}{6}+\dfrac{123}{2}+\dfrac{19}{2}\right)-\left(-\dfrac{95}{7}\right)\times\dfrac{83}{6}\right)-\dfrac{\dfrac{\dfrac{110}{7}}{-11}}{\dfrac{\dfrac{2829}{5}}{\dfrac{25}{2}}}-\left(-\dfrac{41}{4}+\dfrac{1107}{944}\right)\times\left(-\dfrac{440}{119}\right)\times\dfrac{\dfrac{3}{\dfrac{71}{8}}}{-\dfrac{118}{9}}\times\left(\dfrac{110}{7}+\dfrac{95}{7}+\dfrac{118}{9}\right)\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\left(\dfrac{123}{8}-9\right)-\left(-11-\dfrac{116}{7}\times\dfrac{123}{8}\times\left(-11\right)+\dfrac{17}{4}\right)}\\&=&\left(\left(\left(\dfrac{83}{6}+\dfrac{123}{2}+\dfrac{19}{2}\right)-\left(-\dfrac{95}{7}\right)\times\dfrac{83}{6}\right)-\dfrac{\dfrac{\dfrac{110}{7}}{-11}}{\dfrac{\dfrac{2829}{5}}{\dfrac{25}{2}}}-\left(-\dfrac{41}{4}+\dfrac{1107}{944}\right)\times\left(-\dfrac{440}{119}\right)\times\dfrac{\dfrac{24}{71}}{-\dfrac{118}{9}}\times\left(\dfrac{110}{7}+\dfrac{95}{7}+\dfrac{118}{9}\right)\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\left(\dfrac{123}{8}-9\right)-\left(-11-\dfrac{116}{7}\times\dfrac{123}{8}\times\left(-11\right)+\dfrac{17}{4}\right)}\\&=&\left(\left(\left(\dfrac{83}{6}+\dfrac{123}{2}+\dfrac{19}{2}\right)-\left(-\dfrac{95}{7}\right)\times\dfrac{83}{6}\right)-\dfrac{\dfrac{\dfrac{110}{7}}{-11}}{\dfrac{\dfrac{2829}{5}}{\dfrac{25}{2}}}-\left(-\dfrac{41}{4}+\dfrac{1107}{944}\right)\times\left(-\dfrac{440}{119}\right)\times\left(-\dfrac{108}{4189}\right)\times\left(\dfrac{110}{7}+\dfrac{95}{7}+\dfrac{118}{9}\right)\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\left(\dfrac{123}{8}-9\right)-\left(-11-\dfrac{116}{7}\times\dfrac{123}{8}\times\left(-11\right)+\dfrac{17}{4}\right)}\\&=&\left(\left(\left(\dfrac{83}{6}+\dfrac{123}{2}+\dfrac{19}{2}\right)-\left(-\dfrac{95}{7}\right)\times\dfrac{83}{6}\right)-\dfrac{\dfrac{\dfrac{110}{7}}{-11}}{\dfrac{\dfrac{2829}{5}}{\dfrac{25}{2}}}-\left(-\dfrac{41}{4}+\dfrac{1107}{944}\right)\times\left(-\dfrac{440}{119}\right)\times\left(-\dfrac{108}{4189}\right)\times\left(\dfrac{205}{7}+\dfrac{118}{9}\right)\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\left(\dfrac{123}{8}-9\right)-\left(-11-\dfrac{116}{7}\times\dfrac{123}{8}\times\left(-11\right)+\dfrac{17}{4}\right)}\\&=&\left(\left(\left(\dfrac{83}{6}+\dfrac{123}{2}+\dfrac{19}{2}\right)-\left(-\dfrac{95}{7}\right)\times\dfrac{83}{6}\right)-\dfrac{\dfrac{\dfrac{110}{7}}{-11}}{\dfrac{\dfrac{2829}{5}}{\dfrac{25}{2}}}-\left(-\dfrac{41}{4}+\dfrac{1107}{944}\right)\times\left(-\dfrac{440}{119}\right)\times\left(-\dfrac{108}{4189}\right)\times\dfrac{2671}{63}\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\left(\dfrac{123}{8}-9\right)-\left(-11-\dfrac{116}{7}\times\dfrac{123}{8}\times\left(-11\right)+\dfrac{17}{4}\right)}\\&=&\left(\left(\left(\dfrac{83}{6}+\dfrac{123}{2}+\dfrac{19}{2}\right)-\left(-\dfrac{95}{7}\right)\times\dfrac{83}{6}\right)-\dfrac{\dfrac{\dfrac{110}{7}}{-11}}{\dfrac{\dfrac{2829}{5}}{\dfrac{25}{2}}}-\left(-\dfrac{41}{4}+\dfrac{1107}{944}\right)\times\left(-\dfrac{440}{119}\right)\times\left(-\dfrac{108}{4189}\right)\times\dfrac{2671}{63}\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\left(\dfrac{123}{8}-9\right)-\left(-11-\dfrac{3567}{14}\times\left(-11\right)+\dfrac{17}{4}\right)}\\&=&\left(\left(\left(\dfrac{83}{6}+\dfrac{123}{2}+\dfrac{19}{2}\right)-\left(-\dfrac{95}{7}\right)\times\dfrac{83}{6}\right)-\dfrac{\dfrac{\dfrac{110}{7}}{-11}}{\dfrac{\dfrac{2829}{5}}{\dfrac{25}{2}}}-\left(-\dfrac{41}{4}+\dfrac{1107}{944}\right)\times\left(-\dfrac{440}{119}\right)\times\left(-\dfrac{108}{4189}\right)\times\dfrac{2671}{63}\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\left(\dfrac{123}{8}-9\right)-\left(-11+\dfrac{39237}{14}+\dfrac{17}{4}\right)}\\&=&\left(\left(\left(\dfrac{226}{3}+\dfrac{19}{2}\right)-\left(-\dfrac{95}{7}\right)\times\dfrac{83}{6}\right)-\dfrac{\dfrac{\dfrac{110}{7}}{-11}}{\dfrac{\dfrac{2829}{5}}{\dfrac{25}{2}}}-\left(-\dfrac{41}{4}+\dfrac{1107}{944}\right)\times\left(-\dfrac{440}{119}\right)\times\left(-\dfrac{108}{4189}\right)\times\dfrac{2671}{63}\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\left(\dfrac{123}{8}-9\right)-\left(-11+\dfrac{39237}{14}+\dfrac{17}{4}\right)}\\&=&\left(\left(\dfrac{509}{6}-\left(-\dfrac{95}{7}\right)\times\dfrac{83}{6}\right)-\dfrac{\dfrac{\dfrac{110}{7}}{-11}}{\dfrac{\dfrac{2829}{5}}{\dfrac{25}{2}}}-\left(-\dfrac{41}{4}+\dfrac{1107}{944}\right)\times\left(-\dfrac{440}{119}\right)\times\left(-\dfrac{108}{4189}\right)\times\dfrac{2671}{63}\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\left(\dfrac{123}{8}-9\right)-\left(-11+\dfrac{39237}{14}+\dfrac{17}{4}\right)}\\&=&\left(\left(\dfrac{509}{6}+\dfrac{7885}{42}\right)-\dfrac{\dfrac{\dfrac{110}{7}}{-11}}{\dfrac{\dfrac{2829}{5}}{\dfrac{25}{2}}}-\left(-\dfrac{41}{4}+\dfrac{1107}{944}\right)\times\left(-\dfrac{440}{119}\right)\times\left(-\dfrac{108}{4189}\right)\times\dfrac{2671}{63}\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\left(\dfrac{123}{8}-9\right)-\left(-11+\dfrac{39237}{14}+\dfrac{17}{4}\right)}\\&=&\left(\left(\dfrac{509}{6}+\dfrac{7885}{42}\right)-\dfrac{-\dfrac{10}{7}}{\dfrac{\dfrac{2829}{5}}{\dfrac{25}{2}}}-\left(-\dfrac{41}{4}+\dfrac{1107}{944}\right)\times\left(-\dfrac{440}{119}\right)\times\left(-\dfrac{108}{4189}\right)\times\dfrac{2671}{63}\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\left(\dfrac{123}{8}-9\right)-\left(-11+\dfrac{39237}{14}+\dfrac{17}{4}\right)}\\&=&\left(\left(\dfrac{509}{6}+\dfrac{7885}{42}\right)-\dfrac{-\dfrac{10}{7}}{\dfrac{5658}{125}}-\left(-\dfrac{41}{4}+\dfrac{1107}{944}\right)\times\left(-\dfrac{440}{119}\right)\times\left(-\dfrac{108}{4189}\right)\times\dfrac{2671}{63}\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\left(\dfrac{123}{8}-9\right)-\left(-11+\dfrac{39237}{14}+\dfrac{17}{4}\right)}\\&=&\left(\left(\dfrac{509}{6}+\dfrac{7885}{42}\right)-\dfrac{-\dfrac{10}{7}}{\dfrac{5658}{125}}-\left(-\dfrac{8569}{944}\right)\times\left(-\dfrac{440}{119}\right)\times\left(-\dfrac{108}{4189}\right)\times\dfrac{2671}{63}\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\left(\dfrac{123}{8}-9\right)-\left(-11+\dfrac{39237}{14}+\dfrac{17}{4}\right)}\\&=&\left(\left(\dfrac{509}{6}+\dfrac{7885}{42}\right)-\dfrac{-\dfrac{10}{7}}{\dfrac{5658}{125}}-\left(-\dfrac{8569}{944}\right)\times\dfrac{47520}{498491}\times\dfrac{2671}{63}\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\left(\dfrac{123}{8}-9\right)-\left(-11+\dfrac{39237}{14}+\dfrac{17}{4}\right)}\\&=&\left(\left(\dfrac{509}{6}+\dfrac{7885}{42}\right)-\dfrac{-\dfrac{10}{7}}{\dfrac{5658}{125}}-\left(-\dfrac{8569}{944}\right)\times\dfrac{14102880}{3489437}\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\left(\dfrac{123}{8}-9\right)-\left(-11+\dfrac{39237}{14}+\dfrac{17}{4}\right)}\\&=&\left(\left(\dfrac{509}{6}+\dfrac{7885}{42}\right)-\dfrac{-\dfrac{10}{7}}{\dfrac{5658}{125}}-\left(-\dfrac{8569}{944}\right)\times\dfrac{14102880}{3489437}\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\dfrac{51}{8}-\left(-11+\dfrac{39237}{14}+\dfrac{17}{4}\right)}\\&=&\left(\left(\dfrac{509}{6}+\dfrac{7885}{42}\right)-\dfrac{-\dfrac{10}{7}}{\dfrac{5658}{125}}-\left(-\dfrac{8569}{944}\right)\times\dfrac{14102880}{3489437}\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\dfrac{51}{8}-\left(\dfrac{39083}{14}+\dfrac{17}{4}\right)}\\&=&\left(\left(\dfrac{509}{6}+\dfrac{7885}{42}\right)-\dfrac{-\dfrac{10}{7}}{\dfrac{5658}{125}}-\left(-\dfrac{8569}{944}\right)\times\dfrac{14102880}{3489437}\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\dfrac{51}{8}-\dfrac{78285}{28}}\\&=&\left(\dfrac{1908}{7}-\dfrac{-\dfrac{10}{7}}{\dfrac{5658}{125}}-\left(-\dfrac{8569}{944}\right)\times\dfrac{14102880}{3489437}\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\dfrac{51}{8}-\dfrac{78285}{28}}\\&=&\left(\dfrac{1908}{7}+\dfrac{625}{19803}-\left(-\dfrac{8569}{944}\right)\times\dfrac{14102880}{3489437}\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\dfrac{51}{8}-\dfrac{78285}{28}}\\&=&\left(\dfrac{1908}{7}+\dfrac{625}{19803}+\dfrac{120847578720}{3294028528}\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{\dfrac{51}{8}-\dfrac{78285}{28}}\\&=&\left(\dfrac{1908}{7}+\dfrac{625}{19803}+\dfrac{120847578720}{3294028528}\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{-\dfrac{156213}{56}}\\&=&\left(\dfrac{5398357}{19803}+\dfrac{120847578720}{3294028528}\right)+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{-\dfrac{156213}{56}}\\&=&\dfrac{20175486563720656}{65231646939984}+9-\dfrac{\dfrac{\dfrac{110}{7}}{-\dfrac{118}{9}}}{-\dfrac{156213}{56}}\\&=&\dfrac{20175486563720656}{65231646939984}+9-\dfrac{-\dfrac{495}{413}}{-\dfrac{156213}{56}}\\&=&\dfrac{20175486563720656}{65231646939984}+9-\dfrac{440}{1024063}\\&=&\dfrac{20762571386180512}{65231646939984}-\dfrac{440}{1024063}\\&=&\dfrac{2.1262152439522E+22}{6.6801316060301E+19}\\ \end{eqnarray*}