Ataraxy

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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 \[\left(\dfrac{\dfrac{\dfrac{317}{12}}{-4}}{-4}-19+19+\dfrac{79}{9}+19\right)-\dfrac{\dfrac{\left(-\dfrac{100}{3}\right)\times10\times\left(-4\right)\times\left(-4\right)-19}{\left(-\dfrac{100}{3}\right)\times\left(\dfrac{181}{10}+\left(-4\right)\times\dfrac{113}{10}\times11\times\left(-\dfrac{79}{9}\right)+\dfrac{\left(-19\right)\times\left(-4\right)\times\left(-4\right)}{-\dfrac{100}{3}}\right)\times\left(-4\right)}}{\left(10-\left(-4-\dfrac{312}{19}\right)\right)-\left(-4+4+\dfrac{29}{2}\right)-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\]

Cliquer ici pour afficher la solution

Exercice

On a $ X=\left(\dfrac{\dfrac{\dfrac{317}{12}}{-4}}{-4}-19+19+\dfrac{79}{9}+19\right)-\dfrac{\dfrac{\left(-\dfrac{100}{3}\right)\times10\times\left(-4\right)\times\left(-4\right)-19}{\left(-\dfrac{100}{3}\right)\times\left(\dfrac{181}{10}+\left(-4\right)\times\dfrac{113}{10}\times11\times\left(-\dfrac{79}{9}\right)+\dfrac{\left(-19\right)\times\left(-4\right)\times\left(-4\right)}{-\dfrac{100}{3}}\right)\times\left(-4\right)}}{\left(10-\left(-4-\dfrac{312}{19}\right)\right)-\left(-4+4+\dfrac{29}{2}\right)-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}=-\dfrac{146391444241674624}{6167063480131584}$ . Voici le détail : \begin{eqnarray*} X &=&\left(\dfrac{\dfrac{\dfrac{317}{12}}{-4}}{-4}-19+19+\dfrac{79}{9}+19\right)-\dfrac{\dfrac{\left(-\dfrac{100}{3}\right)\times10\times\left(-4\right)\times\left(-4\right)-19}{\left(-\dfrac{100}{3}\right)\times\left(\dfrac{181}{10}+\left(-4\right)\times\dfrac{113}{10}\times\left(-\dfrac{869}{9}\right)+\dfrac{\left(-19\right)\times\left(-4\right)\times\left(-4\right)}{-\dfrac{100}{3}}\right)\times\left(-4\right)}}{\left(10-\left(-4-\dfrac{312}{19}\right)\right)-\left(-4+4+\dfrac{29}{2}\right)-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\left(\dfrac{\dfrac{\dfrac{317}{12}}{-4}}{-4}-19+19+\dfrac{79}{9}+19\right)-\dfrac{\dfrac{\left(-\dfrac{100}{3}\right)\times10\times\left(-4\right)\times\left(-4\right)-19}{\left(-\dfrac{100}{3}\right)\times\left(\dfrac{181}{10}+\left(-4\right)\times\dfrac{113}{10}\times\left(-\dfrac{869}{9}\right)+\dfrac{76\times\left(-4\right)}{-\dfrac{100}{3}}\right)\times\left(-4\right)}}{\left(10-\left(-4-\dfrac{312}{19}\right)\right)-\left(-4+4+\dfrac{29}{2}\right)-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\left(\dfrac{\dfrac{\dfrac{317}{12}}{-4}}{-4}-19+19+\dfrac{79}{9}+19\right)-\dfrac{\dfrac{\left(-\dfrac{100}{3}\right)\times10\times\left(-4\right)\times\left(-4\right)-19}{\left(-\dfrac{100}{3}\right)\times\left(\dfrac{181}{10}+\left(-4\right)\times\dfrac{113}{10}\times\left(-\dfrac{869}{9}\right)+\dfrac{-304}{-\dfrac{100}{3}}\right)\times\left(-4\right)}}{\left(10-\left(-4-\dfrac{312}{19}\right)\right)-\left(-4+4+\dfrac{29}{2}\right)-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\left(\dfrac{\dfrac{\dfrac{317}{12}}{-4}}{-4}-19+19+\dfrac{79}{9}+19\right)-\dfrac{\dfrac{\left(-\dfrac{100}{3}\right)\times10\times\left(-4\right)\times\left(-4\right)-19}{\left(-\dfrac{100}{3}\right)\times\left(\dfrac{181}{10}+\left(-\dfrac{226}{5}\right)\times\left(-\dfrac{869}{9}\right)+\dfrac{-304}{-\dfrac{100}{3}}\right)\times\left(-4\right)}}{\left(10-\left(-4-\dfrac{312}{19}\right)\right)-\left(-4+4+\dfrac{29}{2}\right)-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\left(\dfrac{\dfrac{\dfrac{317}{12}}{-4}}{-4}-19+19+\dfrac{79}{9}+19\right)-\dfrac{\dfrac{\left(-\dfrac{100}{3}\right)\times10\times\left(-4\right)\times\left(-4\right)-19}{\left(-\dfrac{100}{3}\right)\times\left(\dfrac{181}{10}+\dfrac{196394}{45}+\dfrac{-304}{-\dfrac{100}{3}}\right)\times\left(-4\right)}}{\left(10-\left(-4-\dfrac{312}{19}\right)\right)-\left(-4+4+\dfrac{29}{2}\right)-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\left(\dfrac{\dfrac{\dfrac{317}{12}}{-4}}{-4}-19+19+\dfrac{79}{9}+19\right)-\dfrac{\dfrac{\left(-\dfrac{100}{3}\right)\times10\times\left(-4\right)\times\left(-4\right)-19}{\left(-\dfrac{100}{3}\right)\times\left(\dfrac{181}{10}+\dfrac{196394}{45}+\dfrac{228}{25}\right)\times\left(-4\right)}}{\left(10-\left(-4-\dfrac{312}{19}\right)\right)-\left(-4+4+\dfrac{29}{2}\right)-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\left(\dfrac{\dfrac{\dfrac{317}{12}}{-4}}{-4}-19+19+\dfrac{79}{9}+19\right)-\dfrac{\dfrac{\left(-\dfrac{100}{3}\right)\times10\times\left(-4\right)\times\left(-4\right)-19}{\left(-\dfrac{100}{3}\right)\times\left(\dfrac{181}{10}+\dfrac{196394}{45}+\dfrac{228}{25}\right)\times\left(-4\right)}}{\left(10+\dfrac{388}{19}\right)-\left(-4+4+\dfrac{29}{2}\right)-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\left(\dfrac{\dfrac{\dfrac{317}{12}}{-4}}{-4}-19+19+\dfrac{79}{9}+19\right)-\dfrac{\dfrac{\left(-\dfrac{1000}{3}\right)\times\left(-4\right)\times\left(-4\right)-19}{\left(-\dfrac{100}{3}\right)\times\left(\dfrac{181}{10}+\dfrac{196394}{45}+\dfrac{228}{25}\right)\times\left(-4\right)}}{\left(10+\dfrac{388}{19}\right)-\left(-4+4+\dfrac{29}{2}\right)-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\left(\dfrac{\dfrac{\dfrac{317}{12}}{-4}}{-4}-19+19+\dfrac{79}{9}+19\right)-\dfrac{\dfrac{\dfrac{4000}{3}\times\left(-4\right)-19}{\left(-\dfrac{100}{3}\right)\times\left(\dfrac{181}{10}+\dfrac{196394}{45}+\dfrac{228}{25}\right)\times\left(-4\right)}}{\left(10+\dfrac{388}{19}\right)-\left(-4+4+\dfrac{29}{2}\right)-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\left(\dfrac{\dfrac{\dfrac{317}{12}}{-4}}{-4}-19+19+\dfrac{79}{9}+19\right)-\dfrac{\dfrac{-\dfrac{16000}{3}-19}{\left(-\dfrac{100}{3}\right)\times\left(\dfrac{181}{10}+\dfrac{196394}{45}+\dfrac{228}{25}\right)\times\left(-4\right)}}{\left(10+\dfrac{388}{19}\right)-\left(-4+4+\dfrac{29}{2}\right)-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\left(\dfrac{\dfrac{\dfrac{317}{12}}{-4}}{-4}-19+19+\dfrac{79}{9}+19\right)-\dfrac{\dfrac{-\dfrac{16000}{3}-19}{\left(-\dfrac{100}{3}\right)\times\left(\dfrac{394417}{90}+\dfrac{228}{25}\right)\times\left(-4\right)}}{\left(10+\dfrac{388}{19}\right)-\left(-4+4+\dfrac{29}{2}\right)-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\left(\dfrac{\dfrac{\dfrac{317}{12}}{-4}}{-4}-19+19+\dfrac{79}{9}+19\right)-\dfrac{\dfrac{-\dfrac{16000}{3}-19}{\left(-\dfrac{100}{3}\right)\times\dfrac{1976189}{450}\times\left(-4\right)}}{\left(10+\dfrac{388}{19}\right)-\left(-4+4+\dfrac{29}{2}\right)-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\left(\dfrac{\dfrac{\dfrac{317}{12}}{-4}}{-4}-19+19+\dfrac{79}{9}+19\right)-\dfrac{\dfrac{-\dfrac{16000}{3}-19}{\left(-\dfrac{100}{3}\right)\times\dfrac{1976189}{450}\times\left(-4\right)}}{\dfrac{578}{19}-\left(-4+4+\dfrac{29}{2}\right)-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\left(\dfrac{\dfrac{\dfrac{317}{12}}{-4}}{-4}-19+19+\dfrac{79}{9}+19\right)-\dfrac{\dfrac{-\dfrac{16000}{3}-19}{\left(-\dfrac{100}{3}\right)\times\dfrac{1976189}{450}\times\left(-4\right)}}{\dfrac{578}{19}-\left(0+\dfrac{29}{2}\right)-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\left(\dfrac{\dfrac{\dfrac{317}{12}}{-4}}{-4}-19+19+\dfrac{79}{9}+19\right)-\dfrac{\dfrac{-\dfrac{16000}{3}-19}{\left(-\dfrac{100}{3}\right)\times\dfrac{1976189}{450}\times\left(-4\right)}}{\dfrac{578}{19}-\dfrac{29}{2}-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\left(\dfrac{-\dfrac{317}{48}}{-4}-19+19+\dfrac{79}{9}+19\right)-\dfrac{\dfrac{-\dfrac{16000}{3}-19}{\left(-\dfrac{100}{3}\right)\times\dfrac{1976189}{450}\times\left(-4\right)}}{\dfrac{578}{19}-\dfrac{29}{2}-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\left(\dfrac{317}{192}-19+19+\dfrac{79}{9}+19\right)-\dfrac{\dfrac{-\dfrac{16000}{3}-19}{\left(-\dfrac{100}{3}\right)\times\dfrac{1976189}{450}\times\left(-4\right)}}{\dfrac{578}{19}-\dfrac{29}{2}-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\left(\dfrac{317}{192}+0+\dfrac{79}{9}+19\right)-\dfrac{\dfrac{-\dfrac{16000}{3}-19}{\left(-\dfrac{100}{3}\right)\times\dfrac{1976189}{450}\times\left(-4\right)}}{\dfrac{578}{19}-\dfrac{29}{2}-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\left(\dfrac{317}{192}+\dfrac{79}{9}+19\right)-\dfrac{\dfrac{-\dfrac{16000}{3}-19}{\left(-\dfrac{100}{3}\right)\times\dfrac{1976189}{450}\times\left(-4\right)}}{\dfrac{578}{19}-\dfrac{29}{2}-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\left(\dfrac{317}{192}+\dfrac{250}{9}\right)-\dfrac{\dfrac{-\dfrac{16000}{3}-19}{\left(-\dfrac{100}{3}\right)\times\dfrac{1976189}{450}\times\left(-4\right)}}{\dfrac{578}{19}-\dfrac{29}{2}-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\left(\dfrac{317}{192}+\dfrac{250}{9}\right)-\dfrac{\dfrac{-\dfrac{16057}{3}}{\left(-\dfrac{100}{3}\right)\times\dfrac{1976189}{450}\times\left(-4\right)}}{\dfrac{578}{19}-\dfrac{29}{2}-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\left(\dfrac{317}{192}+\dfrac{250}{9}\right)-\dfrac{\dfrac{-\dfrac{16057}{3}}{\left(-\dfrac{3952378}{27}\right)\times\left(-4\right)}}{\dfrac{578}{19}-\dfrac{29}{2}-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\left(\dfrac{317}{192}+\dfrac{250}{9}\right)-\dfrac{\dfrac{-\dfrac{16057}{3}}{\dfrac{15809512}{27}}}{\dfrac{578}{19}-\dfrac{29}{2}-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\left(\dfrac{317}{192}+\dfrac{250}{9}\right)-\dfrac{\dfrac{-\dfrac{16057}{3}}{\dfrac{15809512}{27}}}{\dfrac{605}{38}-8+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\left(\dfrac{317}{192}+\dfrac{250}{9}\right)-\dfrac{\dfrac{-\dfrac{16057}{3}}{\dfrac{15809512}{27}}}{\dfrac{301}{38}+\dfrac{100}{3}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\left(\dfrac{317}{192}+\dfrac{250}{9}\right)-\dfrac{\dfrac{-\dfrac{16057}{3}}{\dfrac{15809512}{27}}}{\dfrac{4703}{114}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\dfrac{16951}{576}-\dfrac{\dfrac{-\dfrac{16057}{3}}{\dfrac{15809512}{27}}}{\dfrac{4703}{114}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\dfrac{16951}{576}-\dfrac{-\dfrac{144513}{15809512}}{\dfrac{4703}{114}}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\dfrac{16951}{576}+\dfrac{16474482}{74352134936}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\dfrac{1260352528601768}{42826829723136}-\dfrac{319}{12}-\dfrac{319}{12}\\&=&\dfrac{1462471661540832}{513921956677632}-\dfrac{319}{12}\\&=&-\dfrac{146391444241674624}{6167063480131584}\\ \end{eqnarray*}