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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 \[-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{121}{7}+6-6+\dfrac{121}{7}-\dfrac{79}{9}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{25}{12}}{-7}}{4}}{-9}}{-9}}{\dfrac{\dfrac{\dfrac{-4}{-\dfrac{25}{12}}}{\dfrac{11}{2}}}{6}}}}{\left(-\dfrac{143}{9}-\dfrac{25}{12}+\dfrac{47}{2}\right)+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{53}{5}-6-9-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\left(-6\right)\times4\times4\times\left(-\dfrac{143}{9}\right)}{\dfrac{11}{6}-\dfrac{11}{2}-6+6}}{4-8}}{\dfrac{11}{6}-\dfrac{79}{9}+\dfrac{121}{7}}\times\dfrac{11}{2}\times\left(-4\right)-4\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{121}{7}+6-6+\dfrac{121}{7}-\dfrac{79}{9}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{25}{12}}{-7}}{4}}{-9}}{-9}}{\dfrac{\dfrac{\dfrac{-4}{-\dfrac{25}{12}}}{\dfrac{11}{2}}}{6}}}}{\left(-\dfrac{143}{9}-\dfrac{25}{12}+\dfrac{47}{2}\right)+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{53}{5}-6-9-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\left(-6\right)\times4\times4\times\left(-\dfrac{143}{9}\right)}{\dfrac{11}{6}-\dfrac{11}{2}-6+6}}{4-8}}{\dfrac{11}{6}-\dfrac{79}{9}+\dfrac{121}{7}}\times\dfrac{11}{2}\times\left(-4\right)-4=\dfrac{118039607040816}{348291900}\) . Voici le détail : \begin{eqnarray*} X &=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{163}{7}-6+\dfrac{121}{7}-\dfrac{79}{9}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{25}{12}}{-7}}{4}}{-9}}{-9}}{\dfrac{\dfrac{\dfrac{-4}{-\dfrac{25}{12}}}{\dfrac{11}{2}}}{6}}}}{\left(-\dfrac{143}{9}-\dfrac{25}{12}+\dfrac{47}{2}\right)+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{53}{5}-6-9-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\left(-6\right)\times4\times4\times\left(-\dfrac{143}{9}\right)}{\dfrac{11}{6}-\dfrac{11}{2}-6+6}}{4-8}}{\dfrac{11}{6}-\dfrac{79}{9}+\dfrac{121}{7}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{163}{7}-6+\dfrac{121}{7}-\dfrac{79}{9}}{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{25}{84}}{4}}{-9}}{-9}}{\dfrac{\dfrac{\dfrac{-4}{-\dfrac{25}{12}}}{\dfrac{11}{2}}}{6}}}}{\left(-\dfrac{143}{9}-\dfrac{25}{12}+\dfrac{47}{2}\right)+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{53}{5}-6-9-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\left(-6\right)\times4\times4\times\left(-\dfrac{143}{9}\right)}{\dfrac{11}{6}-\dfrac{11}{2}-6+6}}{4-8}}{\dfrac{11}{6}-\dfrac{79}{9}+\dfrac{121}{7}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{163}{7}-6+\dfrac{121}{7}-\dfrac{79}{9}}{\dfrac{\dfrac{\dfrac{\dfrac{25}{336}}{-9}}{-9}}{\dfrac{\dfrac{\dfrac{-4}{-\dfrac{25}{12}}}{\dfrac{11}{2}}}{6}}}}{\left(-\dfrac{143}{9}-\dfrac{25}{12}+\dfrac{47}{2}\right)+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{53}{5}-6-9-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\left(-6\right)\times4\times4\times\left(-\dfrac{143}{9}\right)}{\dfrac{11}{6}-\dfrac{11}{2}-6+6}}{4-8}}{\dfrac{11}{6}-\dfrac{79}{9}+\dfrac{121}{7}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{163}{7}-6+\dfrac{121}{7}-\dfrac{79}{9}}{\dfrac{\dfrac{-\dfrac{25}{3024}}{-9}}{\dfrac{\dfrac{\dfrac{-4}{-\dfrac{25}{12}}}{\dfrac{11}{2}}}{6}}}}{\left(-\dfrac{143}{9}-\dfrac{25}{12}+\dfrac{47}{2}\right)+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{53}{5}-6-9-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\left(-6\right)\times4\times4\times\left(-\dfrac{143}{9}\right)}{\dfrac{11}{6}-\dfrac{11}{2}-6+6}}{4-8}}{\dfrac{11}{6}-\dfrac{79}{9}+\dfrac{121}{7}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{163}{7}-6+\dfrac{121}{7}-\dfrac{79}{9}}{\dfrac{\dfrac{-\dfrac{25}{3024}}{-9}}{\dfrac{\dfrac{\dfrac{48}{25}}{\dfrac{11}{2}}}{6}}}}{\left(-\dfrac{143}{9}-\dfrac{25}{12}+\dfrac{47}{2}\right)+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{53}{5}-6-9-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\left(-6\right)\times4\times4\times\left(-\dfrac{143}{9}\right)}{\dfrac{11}{6}-\dfrac{11}{2}-6+6}}{4-8}}{\dfrac{11}{6}-\dfrac{79}{9}+\dfrac{121}{7}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{163}{7}-6+\dfrac{121}{7}-\dfrac{79}{9}}{\dfrac{\dfrac{-\dfrac{25}{3024}}{-9}}{\dfrac{\dfrac{96}{275}}{6}}}}{\left(-\dfrac{143}{9}-\dfrac{25}{12}+\dfrac{47}{2}\right)+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{53}{5}-6-9-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\left(-6\right)\times4\times4\times\left(-\dfrac{143}{9}\right)}{\dfrac{11}{6}-\dfrac{11}{2}-6+6}}{4-8}}{\dfrac{11}{6}-\dfrac{79}{9}+\dfrac{121}{7}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{163}{7}-6+\dfrac{121}{7}-\dfrac{79}{9}}{\dfrac{\dfrac{-\dfrac{25}{3024}}{-9}}{\dfrac{16}{275}}}}{\left(-\dfrac{143}{9}-\dfrac{25}{12}+\dfrac{47}{2}\right)+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{53}{5}-6-9-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\left(-6\right)\times4\times4\times\left(-\dfrac{143}{9}\right)}{\dfrac{11}{6}-\dfrac{11}{2}-6+6}}{4-8}}{\dfrac{11}{6}-\dfrac{79}{9}+\dfrac{121}{7}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{163}{7}-6+\dfrac{121}{7}-\dfrac{79}{9}}{\dfrac{\dfrac{-\dfrac{25}{3024}}{-9}}{\dfrac{16}{275}}}}{\left(-\dfrac{647}{36}+\dfrac{47}{2}\right)+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{53}{5}-6-9-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\left(-6\right)\times4\times4\times\left(-\dfrac{143}{9}\right)}{\dfrac{11}{6}-\dfrac{11}{2}-6+6}}{4-8}}{\dfrac{11}{6}-\dfrac{79}{9}+\dfrac{121}{7}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{163}{7}-6+\dfrac{121}{7}-\dfrac{79}{9}}{\dfrac{\dfrac{-\dfrac{25}{3024}}{-9}}{\dfrac{16}{275}}}}{\dfrac{199}{36}+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{53}{5}-6-9-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\left(-6\right)\times4\times4\times\left(-\dfrac{143}{9}\right)}{\dfrac{11}{6}-\dfrac{11}{2}-6+6}}{4-8}}{\dfrac{11}{6}-\dfrac{79}{9}+\dfrac{121}{7}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{163}{7}-6+\dfrac{121}{7}-\dfrac{79}{9}}{\dfrac{\dfrac{-\dfrac{25}{3024}}{-9}}{\dfrac{16}{275}}}}{\dfrac{199}{36}+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{83}{5}-9-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\left(-6\right)\times4\times4\times\left(-\dfrac{143}{9}\right)}{\dfrac{11}{6}-\dfrac{11}{2}-6+6}}{4-8}}{\dfrac{11}{6}-\dfrac{79}{9}+\dfrac{121}{7}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{163}{7}-6+\dfrac{121}{7}-\dfrac{79}{9}}{\dfrac{\dfrac{-\dfrac{25}{3024}}{-9}}{\dfrac{16}{275}}}}{\dfrac{199}{36}+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{128}{5}-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\left(-6\right)\times4\times4\times\left(-\dfrac{143}{9}\right)}{\dfrac{11}{6}-\dfrac{11}{2}-6+6}}{4-8}}{\dfrac{11}{6}-\dfrac{79}{9}+\dfrac{121}{7}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{163}{7}-6+\dfrac{121}{7}-\dfrac{79}{9}}{\dfrac{\dfrac{-\dfrac{25}{3024}}{-9}}{\dfrac{16}{275}}}}{\dfrac{199}{36}+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{128}{5}-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\left(-24\right)\times4\times\left(-\dfrac{143}{9}\right)}{\dfrac{11}{6}-\dfrac{11}{2}-6+6}}{4-8}}{\dfrac{11}{6}-\dfrac{79}{9}+\dfrac{121}{7}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{163}{7}-6+\dfrac{121}{7}-\dfrac{79}{9}}{\dfrac{\dfrac{-\dfrac{25}{3024}}{-9}}{\dfrac{16}{275}}}}{\dfrac{199}{36}+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{128}{5}-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\left(-96\right)\times\left(-\dfrac{143}{9}\right)}{\dfrac{11}{6}-\dfrac{11}{2}-6+6}}{4-8}}{\dfrac{11}{6}-\dfrac{79}{9}+\dfrac{121}{7}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{163}{7}-6+\dfrac{121}{7}-\dfrac{79}{9}}{\dfrac{\dfrac{-\dfrac{25}{3024}}{-9}}{\dfrac{16}{275}}}}{\dfrac{199}{36}+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{128}{5}-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\dfrac{4576}{3}}{\dfrac{11}{6}-\dfrac{11}{2}-6+6}}{4-8}}{\dfrac{11}{6}-\dfrac{79}{9}+\dfrac{121}{7}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{163}{7}-6+\dfrac{121}{7}-\dfrac{79}{9}}{\dfrac{\dfrac{-\dfrac{25}{3024}}{-9}}{\dfrac{16}{275}}}}{\dfrac{199}{36}+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{128}{5}-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\dfrac{4576}{3}}{-\dfrac{11}{3}-6+6}}{4-8}}{\dfrac{11}{6}-\dfrac{79}{9}+\dfrac{121}{7}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{163}{7}-6+\dfrac{121}{7}-\dfrac{79}{9}}{\dfrac{\dfrac{-\dfrac{25}{3024}}{-9}}{\dfrac{16}{275}}}}{\dfrac{199}{36}+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{128}{5}-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\dfrac{4576}{3}}{-\dfrac{29}{3}+6}}{4-8}}{\dfrac{11}{6}-\dfrac{79}{9}+\dfrac{121}{7}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{163}{7}-6+\dfrac{121}{7}-\dfrac{79}{9}}{\dfrac{\dfrac{-\dfrac{25}{3024}}{-9}}{\dfrac{16}{275}}}}{\dfrac{199}{36}+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{128}{5}-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\dfrac{4576}{3}}{-\dfrac{11}{3}}}{4-8}}{\dfrac{11}{6}-\dfrac{79}{9}+\dfrac{121}{7}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{163}{7}-6+\dfrac{121}{7}-\dfrac{79}{9}}{\dfrac{\dfrac{-\dfrac{25}{3024}}{-9}}{\dfrac{16}{275}}}}{\dfrac{199}{36}+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{128}{5}-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\dfrac{4576}{3}}{-\dfrac{11}{3}}}{-4}}{\dfrac{11}{6}-\dfrac{79}{9}+\dfrac{121}{7}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{163}{7}-6+\dfrac{121}{7}-\dfrac{79}{9}}{\dfrac{\dfrac{-\dfrac{25}{3024}}{-9}}{\dfrac{16}{275}}}}{\dfrac{199}{36}+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{128}{5}-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\dfrac{4576}{3}}{-\dfrac{11}{3}}}{-4}}{-\dfrac{125}{18}+\dfrac{121}{7}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{163}{7}-6+\dfrac{121}{7}-\dfrac{79}{9}}{\dfrac{\dfrac{-\dfrac{25}{3024}}{-9}}{\dfrac{16}{275}}}}{\dfrac{199}{36}+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{128}{5}-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\dfrac{4576}{3}}{-\dfrac{11}{3}}}{-4}}{\dfrac{1303}{126}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{121}{7}+\dfrac{121}{7}-\dfrac{79}{9}}{\dfrac{\dfrac{-\dfrac{25}{3024}}{-9}}{\dfrac{16}{275}}}}{\dfrac{199}{36}+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{128}{5}-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\dfrac{4576}{3}}{-\dfrac{11}{3}}}{-4}}{\dfrac{1303}{126}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{242}{7}-\dfrac{79}{9}}{\dfrac{\dfrac{-\dfrac{25}{3024}}{-9}}{\dfrac{16}{275}}}}{\dfrac{199}{36}+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{128}{5}-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\dfrac{4576}{3}}{-\dfrac{11}{3}}}{-4}}{\dfrac{1303}{126}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{1625}{63}}{\dfrac{\dfrac{-\dfrac{25}{3024}}{-9}}{\dfrac{16}{275}}}}{\dfrac{199}{36}+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{128}{5}-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\dfrac{4576}{3}}{-\dfrac{11}{3}}}{-4}}{\dfrac{1303}{126}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{1625}{63}}{\dfrac{\dfrac{25}{27216}}{\dfrac{16}{275}}}}{\dfrac{199}{36}+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{128}{5}-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\dfrac{4576}{3}}{-\dfrac{11}{3}}}{-4}}{\dfrac{1303}{126}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{1625}{63}}{\dfrac{6875}{435456}}}{\dfrac{199}{36}+\dfrac{25}{12}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{128}{5}-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\dfrac{4576}{3}}{-\dfrac{11}{3}}}{-4}}{\dfrac{1303}{126}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{1625}{63}}{\dfrac{6875}{435456}}}{\dfrac{137}{18}-4}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{128}{5}-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\dfrac{4576}{3}}{-\dfrac{11}{3}}}{-4}}{\dfrac{1303}{126}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{1625}{63}}{\dfrac{6875}{435456}}}{\dfrac{65}{18}}+\dfrac{11}{6}-6+\dfrac{11}{2}+8-\dfrac{128}{5}-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\dfrac{4576}{3}}{-\dfrac{11}{3}}}{-4}}{\dfrac{1303}{126}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{1625}{63}}{\dfrac{6875}{435456}}}{\dfrac{65}{18}}+\dfrac{11}{6}-\dfrac{1}{2}+8-\dfrac{128}{5}-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\dfrac{4576}{3}}{-\dfrac{11}{3}}}{-4}}{\dfrac{1303}{126}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{1625}{63}}{\dfrac{6875}{435456}}}{\dfrac{65}{18}}+\dfrac{11}{6}-\dfrac{1}{2}-\dfrac{88}{5}-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{\dfrac{\dfrac{4576}{3}}{-\dfrac{11}{3}}}{-4}}{\dfrac{1303}{126}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{1625}{63}}{\dfrac{6875}{435456}}}{\dfrac{65}{18}}+\dfrac{11}{6}-\dfrac{1}{2}-\dfrac{88}{5}-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{\dfrac{-416}{-4}}{\dfrac{1303}{126}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{1625}{63}}{\dfrac{6875}{435456}}}{\dfrac{65}{18}}+\dfrac{11}{6}-\dfrac{1}{2}-\dfrac{88}{5}-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{104}{\dfrac{1303}{126}}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{\dfrac{1625}{63}}{\dfrac{6875}{435456}}}{\dfrac{65}{18}}+\dfrac{11}{6}-\dfrac{1}{2}-\dfrac{88}{5}-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{13104}{1303}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{\dfrac{89856}{55}}{\dfrac{65}{18}}+\dfrac{11}{6}-\dfrac{1}{2}-\dfrac{88}{5}-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{13104}{1303}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{124416}{275}+\dfrac{11}{6}-\dfrac{1}{2}-\dfrac{88}{5}-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{13104}{1303}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{124416}{275}+\dfrac{11}{6}-\dfrac{181}{10}-7-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{13104}{1303}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{124416}{275}+\dfrac{11}{6}-\dfrac{251}{10}-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{121}{7}\times\dfrac{13104}{1303}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{124416}{275}+\dfrac{11}{6}-\dfrac{251}{10}-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{226512}{1303}\times\dfrac{11}{2}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{124416}{275}+\dfrac{11}{6}-\dfrac{251}{10}-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\dfrac{1245816}{1303}\times\left(-4\right)-4\\&=&-\dfrac{79}{9}+\dfrac{124416}{275}+\dfrac{11}{6}-\dfrac{251}{10}-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\left(-\dfrac{4983264}{1303}\right)-4\\&=&-\dfrac{79}{9}+\dfrac{749521}{1650}-\dfrac{251}{10}-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\left(-\dfrac{4983264}{1303}\right)-4\\&=&-\dfrac{79}{9}+\dfrac{354053}{825}-6+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\left(-\dfrac{4983264}{1303}\right)-4\\&=&-\dfrac{79}{9}+\dfrac{349103}{825}+\dfrac{11}{2}\times\left(-\dfrac{79}{9}\right)\times\dfrac{11}{6}\times\left(-\dfrac{4983264}{1303}\right)-4\\&=&-\dfrac{79}{9}+\dfrac{349103}{825}+\left(-\dfrac{869}{18}\right)\times\dfrac{11}{6}\times\left(-\dfrac{4983264}{1303}\right)-4\\&=&-\dfrac{79}{9}+\dfrac{349103}{825}+\left(-\dfrac{9559}{108}\right)\times\left(-\dfrac{4983264}{1303}\right)-4\\&=&-\dfrac{79}{9}+\dfrac{349103}{825}+\dfrac{47635020576}{140724}-4\\&=&\dfrac{1025584}{2475}+\dfrac{47635020576}{140724}-4\\&=&\dfrac{118041000208416}{348291900}-4\\&=&\dfrac{118039607040816}{348291900}\\ \end{eqnarray*}