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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 \[\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(\left(\left(\dfrac{41}{12}-5+1\right)-\dfrac{7}{3}-0\times\dfrac{22}{3}\times\dfrac{22}{3}\times\dfrac{27}{2}-\dfrac{-4}{-\dfrac{118}{3}}\right)-\left(\dfrac{27}{2}-\left(6-\dfrac{73}{6}-5\right)-0-\left(-\dfrac{73}{6}-\dfrac{73}{6}\right)\right)-\dfrac{27}{2}-6\right)-6-\left(5\times\left(-\dfrac{73}{6}-\dfrac{41}{12}-5-\dfrac{7}{4}\right)\times\dfrac{59}{12}\times\dfrac{7}{3}-\left(\dfrac{27}{2}-4+5+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{\left(-\dfrac{73}{6}\right)\times1}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(\left(\left(\dfrac{41}{12}-5+1\right)-\dfrac{7}{3}-0\times\dfrac{22}{3}\times\dfrac{22}{3}\times\dfrac{27}{2}-\dfrac{-4}{-\dfrac{118}{3}}\right)-\left(\dfrac{27}{2}-\left(6-\dfrac{73}{6}-5\right)-0-\left(-\dfrac{73}{6}-\dfrac{73}{6}\right)\right)-\dfrac{27}{2}-6\right)-6-\left(5\times\left(-\dfrac{73}{6}-\dfrac{41}{12}-5-\dfrac{7}{4}\right)\times\dfrac{59}{12}\times\dfrac{7}{3}-\left(\dfrac{27}{2}-4+5+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{\left(-\dfrac{73}{6}\right)\times1}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}=-\dfrac{32560920}{136732522755}\) . Voici le détail : \begin{eqnarray*} X &=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(\left(\left(-\dfrac{19}{12}+1\right)-\dfrac{7}{3}-0\times\dfrac{22}{3}\times\dfrac{22}{3}\times\dfrac{27}{2}-\dfrac{-4}{-\dfrac{118}{3}}\right)-\left(\dfrac{27}{2}-\left(6-\dfrac{73}{6}-5\right)-0-\left(-\dfrac{73}{6}-\dfrac{73}{6}\right)\right)-\dfrac{27}{2}-6\right)-6-\left(5\times\left(-\dfrac{73}{6}-\dfrac{41}{12}-5-\dfrac{7}{4}\right)\times\dfrac{59}{12}\times\dfrac{7}{3}-\left(\dfrac{27}{2}-4+5+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{\left(-\dfrac{73}{6}\right)\times1}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(\left(-\dfrac{7}{12}-\dfrac{7}{3}-0\times\dfrac{22}{3}\times\dfrac{22}{3}\times\dfrac{27}{2}-\dfrac{-4}{-\dfrac{118}{3}}\right)-\left(\dfrac{27}{2}-\left(6-\dfrac{73}{6}-5\right)-0-\left(-\dfrac{73}{6}-\dfrac{73}{6}\right)\right)-\dfrac{27}{2}-6\right)-6-\left(5\times\left(-\dfrac{73}{6}-\dfrac{41}{12}-5-\dfrac{7}{4}\right)\times\dfrac{59}{12}\times\dfrac{7}{3}-\left(\dfrac{27}{2}-4+5+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{\left(-\dfrac{73}{6}\right)\times1}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(\left(-\dfrac{7}{12}-\dfrac{7}{3}-0\times\dfrac{22}{3}\times\dfrac{27}{2}-\dfrac{-4}{-\dfrac{118}{3}}\right)-\left(\dfrac{27}{2}-\left(6-\dfrac{73}{6}-5\right)-0-\left(-\dfrac{73}{6}-\dfrac{73}{6}\right)\right)-\dfrac{27}{2}-6\right)-6-\left(5\times\left(-\dfrac{73}{6}-\dfrac{41}{12}-5-\dfrac{7}{4}\right)\times\dfrac{59}{12}\times\dfrac{7}{3}-\left(\dfrac{27}{2}-4+5+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{\left(-\dfrac{73}{6}\right)\times1}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(\left(-\dfrac{7}{12}-\dfrac{7}{3}-0\times\dfrac{27}{2}-\dfrac{-4}{-\dfrac{118}{3}}\right)-\left(\dfrac{27}{2}-\left(6-\dfrac{73}{6}-5\right)-0-\left(-\dfrac{73}{6}-\dfrac{73}{6}\right)\right)-\dfrac{27}{2}-6\right)-6-\left(5\times\left(-\dfrac{73}{6}-\dfrac{41}{12}-5-\dfrac{7}{4}\right)\times\dfrac{59}{12}\times\dfrac{7}{3}-\left(\dfrac{27}{2}-4+5+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{\left(-\dfrac{73}{6}\right)\times1}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(\left(-\dfrac{7}{12}-\dfrac{7}{3}-0-\dfrac{-4}{-\dfrac{118}{3}}\right)-\left(\dfrac{27}{2}-\left(6-\dfrac{73}{6}-5\right)-0-\left(-\dfrac{73}{6}-\dfrac{73}{6}\right)\right)-\dfrac{27}{2}-6\right)-6-\left(5\times\left(-\dfrac{73}{6}-\dfrac{41}{12}-5-\dfrac{7}{4}\right)\times\dfrac{59}{12}\times\dfrac{7}{3}-\left(\dfrac{27}{2}-4+5+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{\left(-\dfrac{73}{6}\right)\times1}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(\left(-\dfrac{7}{12}-\dfrac{7}{3}-0-\dfrac{6}{59}\right)-\left(\dfrac{27}{2}-\left(6-\dfrac{73}{6}-5\right)-0-\left(-\dfrac{73}{6}-\dfrac{73}{6}\right)\right)-\dfrac{27}{2}-6\right)-6-\left(5\times\left(-\dfrac{73}{6}-\dfrac{41}{12}-5-\dfrac{7}{4}\right)\times\dfrac{59}{12}\times\dfrac{7}{3}-\left(\dfrac{27}{2}-4+5+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{\left(-\dfrac{73}{6}\right)\times1}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(\left(-\dfrac{7}{12}-\dfrac{7}{3}-0-\dfrac{6}{59}\right)-\left(\dfrac{27}{2}-\left(-\dfrac{37}{6}-5\right)-0-\left(-\dfrac{73}{6}-\dfrac{73}{6}\right)\right)-\dfrac{27}{2}-6\right)-6-\left(5\times\left(-\dfrac{73}{6}-\dfrac{41}{12}-5-\dfrac{7}{4}\right)\times\dfrac{59}{12}\times\dfrac{7}{3}-\left(\dfrac{27}{2}-4+5+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{\left(-\dfrac{73}{6}\right)\times1}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(\left(-\dfrac{7}{12}-\dfrac{7}{3}-0-\dfrac{6}{59}\right)-\left(\dfrac{27}{2}+\dfrac{67}{6}-0-\left(-\dfrac{73}{6}-\dfrac{73}{6}\right)\right)-\dfrac{27}{2}-6\right)-6-\left(5\times\left(-\dfrac{73}{6}-\dfrac{41}{12}-5-\dfrac{7}{4}\right)\times\dfrac{59}{12}\times\dfrac{7}{3}-\left(\dfrac{27}{2}-4+5+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{\left(-\dfrac{73}{6}\right)\times1}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(\left(-\dfrac{7}{12}-\dfrac{7}{3}-0-\dfrac{6}{59}\right)-\left(\dfrac{27}{2}+\dfrac{67}{6}-0+\dfrac{73}{3}\right)-\dfrac{27}{2}-6\right)-6-\left(5\times\left(-\dfrac{73}{6}-\dfrac{41}{12}-5-\dfrac{7}{4}\right)\times\dfrac{59}{12}\times\dfrac{7}{3}-\left(\dfrac{27}{2}-4+5+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{\left(-\dfrac{73}{6}\right)\times1}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(\left(-\dfrac{7}{12}-\dfrac{7}{3}-0-\dfrac{6}{59}\right)-\left(\dfrac{27}{2}+\dfrac{67}{6}-0+\dfrac{73}{3}\right)-\dfrac{27}{2}-6\right)-6-\left(5\times\left(-\dfrac{187}{12}-5-\dfrac{7}{4}\right)\times\dfrac{59}{12}\times\dfrac{7}{3}-\left(\dfrac{27}{2}-4+5+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{\left(-\dfrac{73}{6}\right)\times1}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(\left(-\dfrac{7}{12}-\dfrac{7}{3}-0-\dfrac{6}{59}\right)-\left(\dfrac{27}{2}+\dfrac{67}{6}-0+\dfrac{73}{3}\right)-\dfrac{27}{2}-6\right)-6-\left(5\times\left(-\dfrac{247}{12}-\dfrac{7}{4}\right)\times\dfrac{59}{12}\times\dfrac{7}{3}-\left(\dfrac{27}{2}-4+5+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{\left(-\dfrac{73}{6}\right)\times1}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(\left(-\dfrac{7}{12}-\dfrac{7}{3}-0-\dfrac{6}{59}\right)-\left(\dfrac{27}{2}+\dfrac{67}{6}-0+\dfrac{73}{3}\right)-\dfrac{27}{2}-6\right)-6-\left(5\times\left(-\dfrac{67}{3}\right)\times\dfrac{59}{12}\times\dfrac{7}{3}-\left(\dfrac{27}{2}-4+5+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{\left(-\dfrac{73}{6}\right)\times1}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(\left(-\dfrac{7}{12}-\dfrac{7}{3}-0-\dfrac{6}{59}\right)-\left(\dfrac{27}{2}+\dfrac{67}{6}-0+\dfrac{73}{3}\right)-\dfrac{27}{2}-6\right)-6-\left(5\times\left(-\dfrac{67}{3}\right)\times\dfrac{59}{12}\times\dfrac{7}{3}-\left(\dfrac{27}{2}+1+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{\left(-\dfrac{73}{6}\right)\times1}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(\left(-\dfrac{7}{12}-\dfrac{7}{3}-0-\dfrac{6}{59}\right)-\left(\dfrac{27}{2}+\dfrac{67}{6}-0+\dfrac{73}{3}\right)-\dfrac{27}{2}-6\right)-6-\left(5\times\left(-\dfrac{67}{3}\right)\times\dfrac{59}{12}\times\dfrac{7}{3}-\left(\dfrac{27}{2}+1+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{-\dfrac{73}{6}}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(\left(-\dfrac{35}{12}-0-\dfrac{6}{59}\right)-\left(\dfrac{27}{2}+\dfrac{67}{6}-0+\dfrac{73}{3}\right)-\dfrac{27}{2}-6\right)-6-\left(5\times\left(-\dfrac{67}{3}\right)\times\dfrac{59}{12}\times\dfrac{7}{3}-\left(\dfrac{27}{2}+1+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{-\dfrac{73}{6}}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(\left(-\dfrac{35}{12}-\dfrac{6}{59}\right)-\left(\dfrac{27}{2}+\dfrac{67}{6}-0+\dfrac{73}{3}\right)-\dfrac{27}{2}-6\right)-6-\left(5\times\left(-\dfrac{67}{3}\right)\times\dfrac{59}{12}\times\dfrac{7}{3}-\left(\dfrac{27}{2}+1+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{-\dfrac{73}{6}}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(-\dfrac{2137}{708}-\left(\dfrac{27}{2}+\dfrac{67}{6}-0+\dfrac{73}{3}\right)-\dfrac{27}{2}-6\right)-6-\left(5\times\left(-\dfrac{67}{3}\right)\times\dfrac{59}{12}\times\dfrac{7}{3}-\left(\dfrac{27}{2}+1+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{-\dfrac{73}{6}}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(-\dfrac{2137}{708}-\left(\dfrac{74}{3}-0+\dfrac{73}{3}\right)-\dfrac{27}{2}-6\right)-6-\left(5\times\left(-\dfrac{67}{3}\right)\times\dfrac{59}{12}\times\dfrac{7}{3}-\left(\dfrac{27}{2}+1+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{-\dfrac{73}{6}}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(-\dfrac{2137}{708}-\left(\dfrac{74}{3}+\dfrac{73}{3}\right)-\dfrac{27}{2}-6\right)-6-\left(5\times\left(-\dfrac{67}{3}\right)\times\dfrac{59}{12}\times\dfrac{7}{3}-\left(\dfrac{27}{2}+1+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{-\dfrac{73}{6}}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(-\dfrac{2137}{708}-49-\dfrac{27}{2}-6\right)-6-\left(5\times\left(-\dfrac{67}{3}\right)\times\dfrac{59}{12}\times\dfrac{7}{3}-\left(\dfrac{27}{2}+1+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{-\dfrac{73}{6}}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(-\dfrac{2137}{708}-49-\dfrac{27}{2}-6\right)-6-\left(\left(-\dfrac{335}{3}\right)\times\dfrac{59}{12}\times\dfrac{7}{3}-\left(\dfrac{27}{2}+1+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{-\dfrac{73}{6}}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(-\dfrac{2137}{708}-49-\dfrac{27}{2}-6\right)-6-\left(\left(-\dfrac{19765}{36}\right)\times\dfrac{7}{3}-\left(\dfrac{27}{2}+1+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{-\dfrac{73}{6}}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(-\dfrac{2137}{708}-49-\dfrac{27}{2}-6\right)-6-\left(-\dfrac{138355}{108}-\left(\dfrac{27}{2}+1+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{-\dfrac{73}{6}}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(-\dfrac{2137}{708}-49-\dfrac{27}{2}-6\right)-6-\left(-\dfrac{138355}{108}-\left(\dfrac{29}{2}+1\right)-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{-\dfrac{73}{6}}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(-\dfrac{2137}{708}-49-\dfrac{27}{2}-6\right)-6-\left(-\dfrac{138355}{108}-\dfrac{31}{2}-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{-5}{-\dfrac{73}{6}}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(-\dfrac{2137}{708}-49-\dfrac{27}{2}-6\right)-6-\left(-\dfrac{138355}{108}-\dfrac{31}{2}-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{\dfrac{30}{73}}{\dfrac{7}{3}}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(-\dfrac{2137}{708}-49-\dfrac{27}{2}-6\right)-6-\left(-\dfrac{138355}{108}-\dfrac{31}{2}-0\right)}}{\left(6+6\right)-0-\left(\dfrac{\dfrac{90}{511}}{\dfrac{27}{2}}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{\dfrac{\dfrac{7}{3}}{\dfrac{7}{3}}-\left(-\dfrac{2137}{708}-49-\dfrac{27}{2}-6\right)-6-\left(-\dfrac{138355}{108}-\dfrac{31}{2}-0\right)}}{\left(6+6\right)-0-\left(\dfrac{20}{1533}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{1-\left(-\dfrac{2137}{708}-49-\dfrac{27}{2}-6\right)-6-\left(-\dfrac{138355}{108}-\dfrac{31}{2}-0\right)}}{\left(6+6\right)-0-\left(\dfrac{20}{1533}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{1-\left(-\dfrac{36829}{708}-\dfrac{27}{2}-6\right)-6-\left(-\dfrac{138355}{108}-\dfrac{31}{2}-0\right)}}{\left(6+6\right)-0-\left(\dfrac{20}{1533}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{1-\left(-\dfrac{46387}{708}-6\right)-6-\left(-\dfrac{138355}{108}-\dfrac{31}{2}-0\right)}}{\left(6+6\right)-0-\left(\dfrac{20}{1533}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{1+\dfrac{50635}{708}-6-\left(-\dfrac{138355}{108}-\dfrac{31}{2}-0\right)}}{\left(6+6\right)-0-\left(\dfrac{20}{1533}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{1+\dfrac{50635}{708}-6-\left(-\dfrac{140029}{108}-0\right)}}{\left(6+6\right)-0-\left(\dfrac{20}{1533}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{1+\dfrac{50635}{708}-6+\dfrac{140029}{108}}}{\left(6+6\right)-0-\left(\dfrac{20}{1533}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{1+\dfrac{50635}{708}-6+\dfrac{140029}{108}}}{12-0-\left(\dfrac{20}{1533}-\dfrac{41}{12}\right)}\\&=&\dfrac{\dfrac{-5}{1+\dfrac{50635}{708}-6+\dfrac{140029}{108}}}{12-0+\dfrac{6957}{2044}}\\&=&\dfrac{\dfrac{-5}{\dfrac{51343}{708}-6+\dfrac{140029}{108}}}{12-0+\dfrac{6957}{2044}}\\&=&\dfrac{\dfrac{-5}{\dfrac{47095}{708}+\dfrac{140029}{108}}}{12-0+\dfrac{6957}{2044}}\\&=&\dfrac{\dfrac{-5}{\dfrac{4342783}{3186}}}{12-0+\dfrac{6957}{2044}}\\&=&\dfrac{\dfrac{-5}{\dfrac{4342783}{3186}}}{12+\dfrac{6957}{2044}}\\&=&\dfrac{\dfrac{-5}{\dfrac{4342783}{3186}}}{\dfrac{31485}{2044}}\\&=&\dfrac{-\dfrac{15930}{4342783}}{\dfrac{31485}{2044}}\\&=&-\dfrac{32560920}{136732522755}\\ \end{eqnarray*}