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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 \[-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{\dfrac{76}{15}}{\dfrac{9}{3}}}{\dfrac{\dfrac{-11-\dfrac{76}{15}\times\dfrac{187}{10}\times\dfrac{50}{19}\times\left(-\dfrac{264}{19}\right)-\dfrac{27}{5}}{\dfrac{187}{10}}}{\left(\dfrac{27}{5}-\dfrac{89}{8}\right)\times\left(-\dfrac{311}{8}-\dfrac{38}{3}\right)}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{209}{18}}{-\dfrac{89}{8}}}{-\dfrac{311}{8}}}{\dfrac{58}{5}}}{-\dfrac{311}{8}}}{\dfrac{-\dfrac{38}{3}}{-\dfrac{89}{8}}\times\dfrac{58}{5}\times\dfrac{204}{13}\times\left(-\dfrac{89}{8}\right)\times\dfrac{27}{5}\times\left(-\dfrac{343}{4}\right)\times\left(-\dfrac{311}{8}\right)}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{\dfrac{76}{15}}{\dfrac{9}{3}}}{\dfrac{\dfrac{-11-\dfrac{76}{15}\times\dfrac{187}{10}\times\dfrac{50}{19}\times\left(-\dfrac{264}{19}\right)-\dfrac{27}{5}}{\dfrac{187}{10}}}{\left(\dfrac{27}{5}-\dfrac{89}{8}\right)\times\left(-\dfrac{311}{8}-\dfrac{38}{3}\right)}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{209}{18}}{-\dfrac{89}{8}}}{-\dfrac{311}{8}}}{\dfrac{58}{5}}}{-\dfrac{311}{8}}}{\dfrac{-\dfrac{38}{3}}{-\dfrac{89}{8}}\times\dfrac{58}{5}\times\dfrac{204}{13}\times\left(-\dfrac{89}{8}\right)\times\dfrac{27}{5}\times\left(-\dfrac{343}{4}\right)\times\left(-\dfrac{311}{8}\right)}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}=-\dfrac{6.756915460312E+42}{8.8890441942981E+40}\) . Voici le détail : \begin{eqnarray*} X &=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{\dfrac{76}{15}}{\dfrac{9}{3}}}{\dfrac{\dfrac{-11-\dfrac{7106}{75}\times\dfrac{50}{19}\times\left(-\dfrac{264}{19}\right)-\dfrac{27}{5}}{\dfrac{187}{10}}}{\left(\dfrac{27}{5}-\dfrac{89}{8}\right)\times\left(-\dfrac{311}{8}-\dfrac{38}{3}\right)}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{209}{18}}{-\dfrac{89}{8}}}{-\dfrac{311}{8}}}{\dfrac{58}{5}}}{-\dfrac{311}{8}}}{\dfrac{-\dfrac{38}{3}}{-\dfrac{89}{8}}\times\dfrac{58}{5}\times\dfrac{204}{13}\times\left(-\dfrac{89}{8}\right)\times\dfrac{27}{5}\times\left(-\dfrac{343}{4}\right)\times\left(-\dfrac{311}{8}\right)}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{\dfrac{76}{15}}{\dfrac{9}{3}}}{\dfrac{\dfrac{-11-\dfrac{748}{3}\times\left(-\dfrac{264}{19}\right)-\dfrac{27}{5}}{\dfrac{187}{10}}}{\left(\dfrac{27}{5}-\dfrac{89}{8}\right)\times\left(-\dfrac{311}{8}-\dfrac{38}{3}\right)}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{209}{18}}{-\dfrac{89}{8}}}{-\dfrac{311}{8}}}{\dfrac{58}{5}}}{-\dfrac{311}{8}}}{\dfrac{-\dfrac{38}{3}}{-\dfrac{89}{8}}\times\dfrac{58}{5}\times\dfrac{204}{13}\times\left(-\dfrac{89}{8}\right)\times\dfrac{27}{5}\times\left(-\dfrac{343}{4}\right)\times\left(-\dfrac{311}{8}\right)}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{\dfrac{76}{15}}{\dfrac{9}{3}}}{\dfrac{\dfrac{-11+\dfrac{65824}{19}-\dfrac{27}{5}}{\dfrac{187}{10}}}{\left(\dfrac{27}{5}-\dfrac{89}{8}\right)\times\left(-\dfrac{311}{8}-\dfrac{38}{3}\right)}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{209}{18}}{-\dfrac{89}{8}}}{-\dfrac{311}{8}}}{\dfrac{58}{5}}}{-\dfrac{311}{8}}}{\dfrac{-\dfrac{38}{3}}{-\dfrac{89}{8}}\times\dfrac{58}{5}\times\dfrac{204}{13}\times\left(-\dfrac{89}{8}\right)\times\dfrac{27}{5}\times\left(-\dfrac{343}{4}\right)\times\left(-\dfrac{311}{8}\right)}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{\dfrac{76}{15}}{\dfrac{9}{3}}}{\dfrac{\dfrac{-11+\dfrac{65824}{19}-\dfrac{27}{5}}{\dfrac{187}{10}}}{-\dfrac{229}{40}\times\left(-\dfrac{311}{8}-\dfrac{38}{3}\right)}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{209}{18}}{-\dfrac{89}{8}}}{-\dfrac{311}{8}}}{\dfrac{58}{5}}}{-\dfrac{311}{8}}}{\dfrac{-\dfrac{38}{3}}{-\dfrac{89}{8}}\times\dfrac{58}{5}\times\dfrac{204}{13}\times\left(-\dfrac{89}{8}\right)\times\dfrac{27}{5}\times\left(-\dfrac{343}{4}\right)\times\left(-\dfrac{311}{8}\right)}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{\dfrac{76}{15}}{\dfrac{9}{3}}}{\dfrac{\dfrac{-11+\dfrac{65824}{19}-\dfrac{27}{5}}{\dfrac{187}{10}}}{-\dfrac{229}{40}\times-\dfrac{1237}{24}}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{209}{18}}{-\dfrac{89}{8}}}{-\dfrac{311}{8}}}{\dfrac{58}{5}}}{-\dfrac{311}{8}}}{\dfrac{-\dfrac{38}{3}}{-\dfrac{89}{8}}\times\dfrac{58}{5}\times\dfrac{204}{13}\times\left(-\dfrac{89}{8}\right)\times\dfrac{27}{5}\times\left(-\dfrac{343}{4}\right)\times\left(-\dfrac{311}{8}\right)}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{\dfrac{76}{15}}{\dfrac{9}{3}}}{\dfrac{\dfrac{-11+\dfrac{65824}{19}-\dfrac{27}{5}}{\dfrac{187}{10}}}{-\dfrac{229}{40}\times-\dfrac{1237}{24}}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{209}{18}}{-\dfrac{89}{8}}}{-\dfrac{311}{8}}}{\dfrac{58}{5}}}{-\dfrac{311}{8}}}{\dfrac{304}{267}\times\dfrac{58}{5}\times\dfrac{204}{13}\times\left(-\dfrac{89}{8}\right)\times\dfrac{27}{5}\times\left(-\dfrac{343}{4}\right)\times\left(-\dfrac{311}{8}\right)}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{\dfrac{76}{15}}{\dfrac{9}{3}}}{\dfrac{\dfrac{-11+\dfrac{65824}{19}-\dfrac{27}{5}}{\dfrac{187}{10}}}{-\dfrac{229}{40}\times-\dfrac{1237}{24}}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{209}{18}}{-\dfrac{89}{8}}}{-\dfrac{311}{8}}}{\dfrac{58}{5}}}{-\dfrac{311}{8}}}{\dfrac{304}{267}\times\dfrac{58}{5}\times\left(-\dfrac{4539}{26}\right)\times\dfrac{27}{5}\times\left(-\dfrac{343}{4}\right)\times\left(-\dfrac{311}{8}\right)}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{\dfrac{76}{15}}{\dfrac{9}{3}}}{\dfrac{\dfrac{-11+\dfrac{65824}{19}-\dfrac{27}{5}}{\dfrac{187}{10}}}{-\dfrac{229}{40}\times-\dfrac{1237}{24}}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{209}{18}}{-\dfrac{89}{8}}}{-\dfrac{311}{8}}}{\dfrac{58}{5}}}{-\dfrac{311}{8}}}{\dfrac{304}{267}\times\dfrac{58}{5}\times\left(-\dfrac{122553}{130}\right)\times\left(-\dfrac{343}{4}\right)\times\left(-\dfrac{311}{8}\right)}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{\dfrac{76}{15}}{\dfrac{9}{3}}}{\dfrac{\dfrac{-11+\dfrac{65824}{19}-\dfrac{27}{5}}{\dfrac{187}{10}}}{-\dfrac{229}{40}\times-\dfrac{1237}{24}}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{209}{18}}{-\dfrac{89}{8}}}{-\dfrac{311}{8}}}{\dfrac{58}{5}}}{-\dfrac{311}{8}}}{\dfrac{304}{267}\times\dfrac{58}{5}\times\dfrac{42035679}{520}\times\left(-\dfrac{311}{8}\right)}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{\dfrac{76}{15}}{\dfrac{9}{3}}}{\dfrac{\dfrac{-11+\dfrac{65824}{19}-\dfrac{27}{5}}{\dfrac{187}{10}}}{-\dfrac{229}{40}\times-\dfrac{1237}{24}}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{209}{18}}{-\dfrac{89}{8}}}{-\dfrac{311}{8}}}{\dfrac{58}{5}}}{-\dfrac{311}{8}}}{\dfrac{304}{267}\times\dfrac{58}{5}\times\left(-\dfrac{13073096169}{4160}\right)}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{\dfrac{76}{15}}{\dfrac{9}{3}}}{\dfrac{\dfrac{\dfrac{65615}{19}-\dfrac{27}{5}}{\dfrac{187}{10}}}{-\dfrac{229}{40}\times-\dfrac{1237}{24}}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{209}{18}}{-\dfrac{89}{8}}}{-\dfrac{311}{8}}}{\dfrac{58}{5}}}{-\dfrac{311}{8}}}{\dfrac{304}{267}\times\dfrac{58}{5}\times\left(-\dfrac{13073096169}{4160}\right)}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{\dfrac{76}{15}}{\dfrac{9}{3}}}{\dfrac{\dfrac{\dfrac{327562}{95}}{\dfrac{187}{10}}}{-\dfrac{229}{40}\times-\dfrac{1237}{24}}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{209}{18}}{-\dfrac{89}{8}}}{-\dfrac{311}{8}}}{\dfrac{58}{5}}}{-\dfrac{311}{8}}}{\dfrac{304}{267}\times\dfrac{58}{5}\times\left(-\dfrac{13073096169}{4160}\right)}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{\dfrac{76}{15}}{\dfrac{9}{3}}}{\dfrac{\dfrac{\dfrac{327562}{95}}{\dfrac{187}{10}}}{\dfrac{283273}{960}}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{\dfrac{209}{18}}{-\dfrac{89}{8}}}{-\dfrac{311}{8}}}{\dfrac{58}{5}}}{-\dfrac{311}{8}}}{\dfrac{304}{267}\times\dfrac{58}{5}\times\left(-\dfrac{13073096169}{4160}\right)}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{\dfrac{76}{15}}{\dfrac{9}{3}}}{\dfrac{\dfrac{\dfrac{327562}{95}}{\dfrac{187}{10}}}{\dfrac{283273}{960}}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{836}{801}}{-\dfrac{311}{8}}}{\dfrac{58}{5}}}{-\dfrac{311}{8}}}{\dfrac{304}{267}\times\dfrac{58}{5}\times\left(-\dfrac{13073096169}{4160}\right)}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{\dfrac{76}{15}}{\dfrac{9}{3}}}{\dfrac{\dfrac{\dfrac{327562}{95}}{\dfrac{187}{10}}}{\dfrac{283273}{960}}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{836}{801}}{-\dfrac{311}{8}}}{\dfrac{58}{5}}}{-\dfrac{311}{8}}}{\dfrac{17632}{1335}\times\left(-\dfrac{13073096169}{4160}\right)}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{\dfrac{76}{15}}{\dfrac{9}{3}}}{\dfrac{\dfrac{\dfrac{327562}{95}}{\dfrac{187}{10}}}{\dfrac{283273}{960}}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{836}{801}}{-\dfrac{311}{8}}}{\dfrac{58}{5}}}{-\dfrac{311}{8}}}{-\dfrac{230504831651808}{5553600}}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{\dfrac{76}{15}}{3}}{\dfrac{\dfrac{\dfrac{327562}{95}}{\dfrac{187}{10}}}{\dfrac{283273}{960}}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{836}{801}}{-\dfrac{311}{8}}}{\dfrac{58}{5}}}{-\dfrac{311}{8}}}{-\dfrac{230504831651808}{5553600}}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{\dfrac{76}{15}}{3}}{\dfrac{\dfrac{655124}{3553}}{\dfrac{283273}{960}}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{836}{801}}{-\dfrac{311}{8}}}{\dfrac{58}{5}}}{-\dfrac{311}{8}}}{-\dfrac{230504831651808}{5553600}}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{\dfrac{76}{15}}{3}}{\dfrac{628919040}{1006468969}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{-\dfrac{836}{801}}{-\dfrac{311}{8}}}{\dfrac{58}{5}}}{-\dfrac{311}{8}}}{-\dfrac{230504831651808}{5553600}}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{\dfrac{76}{15}}{3}}{\dfrac{628919040}{1006468969}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{\dfrac{\dfrac{\dfrac{6688}{249111}}{\dfrac{58}{5}}}{-\dfrac{311}{8}}}{-\dfrac{230504831651808}{5553600}}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{\dfrac{76}{15}}{3}}{\dfrac{628919040}{1006468969}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{\dfrac{\dfrac{16720}{7224219}}{-\dfrac{311}{8}}}{-\dfrac{230504831651808}{5553600}}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{\dfrac{76}{15}}{3}}{\dfrac{628919040}{1006468969}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{-\dfrac{133760}{2246732109}}{-\dfrac{230504831651808}{5553600}}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{\dfrac{76}{15}}{3}}{\dfrac{628919040}{1006468969}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{742849536000}{5.1788260655176E+23}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{\dfrac{76}{45}}{\dfrac{628919040}{1006468969}}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{742849536000}{5.1788260655176E+23}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{76491641644}{28301356800}-\dfrac{27}{5}-\left(-\dfrac{264}{19}\right)\times\dfrac{742849536000}{5.1788260655176E+23}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{76491641644}{28301356800}-\dfrac{27}{5}+\dfrac{196112277504000}{9.8397695244834E+24}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(-\dfrac{381678425380}{141506784000}+\dfrac{196112277504000}{9.8397695244834E+24}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(-\dfrac{3.7556277381792E+36}{1.3923941407109E+36}+\dfrac{343}{4}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\left(\dfrac{4.6256867931111E+38}{5.5695765628434E+36}-\dfrac{23}{7}\right)-\dfrac{58}{5}\\&=&-\dfrac{38}{3}+\dfrac{113}{8}+\dfrac{264}{19}-\dfrac{3.1098804942323E+39}{3.8987035939904E+37}-\dfrac{58}{5}\\&=&\dfrac{35}{24}+\dfrac{264}{19}-\dfrac{3.1098804942323E+39}{3.8987035939904E+37}-\dfrac{58}{5}\\&=&\dfrac{7001}{456}-\dfrac{3.1098804942323E+39}{3.8987035939904E+37}-\dfrac{58}{5}\\&=&-\dfrac{1.1451572667547E+42}{1.7778088388596E+40}-\dfrac{58}{5}\\&=&-\dfrac{6.756915460312E+42}{8.8890441942981E+40}\\ \end{eqnarray*}