L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
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La correction se trouve en bas de page.
Exercice
Calculer \[-\dfrac{97}{5}-\dfrac{\dfrac{\left(\dfrac{62}{3}-4\right)\times\left(-\dfrac{180}{7}-\left(\dfrac{99}{4}+6+20\right)\right)\times\left(-15\right)}{\dfrac{180}{7}}}{-\dfrac{113}{6}}+4-\dfrac{13}{18}-\left(\left(-\dfrac{113}{7}-\dfrac{18}{5}\right)-4\right)-\dfrac{147}{4}-\dfrac{263}{19}-20\]
Cliquer ici pour afficher la solution
Exercice
On a \( X=-\dfrac{97}{5}-\dfrac{\dfrac{\left(\dfrac{62}{3}-4\right)\times\left(-\dfrac{180}{7}-\left(\dfrac{99}{4}+6+20\right)\right)\times\left(-15\right)}{\dfrac{180}{7}}}{-\dfrac{113}{6}}+4-\dfrac{13}{18}-\left(\left(-\dfrac{113}{7}-\dfrac{18}{5}\right)-4\right)-\dfrac{147}{4}-\dfrac{263}{19}-20=-\dfrac{31784653}{1352610}\) . Voici le détail :
\begin{eqnarray*}
X &=&-\dfrac{97}{5}-\dfrac{\dfrac{\left(\dfrac{62}{3}-4\right)\times\left(-\dfrac{180}{7}-\left(\dfrac{123}{4}+20\right)\right)\times\left(-15\right)}{\dfrac{180}{7}}}{-\dfrac{113}{6}}+4-\dfrac{13}{18}-\left(\left(-\dfrac{113}{7}-\dfrac{18}{5}\right)-4\right)-\dfrac{147}{4}-\dfrac{263}{19}-20\\&=&-\dfrac{97}{5}-\dfrac{\dfrac{\left(\dfrac{62}{3}-4\right)\times\left(-\dfrac{180}{7}-\dfrac{203}{4}\right)\times\left(-15\right)}{\dfrac{180}{7}}}{-\dfrac{113}{6}}+4-\dfrac{13}{18}-\left(\left(-\dfrac{113}{7}-\dfrac{18}{5}\right)-4\right)-\dfrac{147}{4}-\dfrac{263}{19}-20\\&=&-\dfrac{97}{5}-\dfrac{\dfrac{\dfrac{50}{3}\times\left(-\dfrac{180}{7}-\dfrac{203}{4}\right)\times\left(-15\right)}{\dfrac{180}{7}}}{-\dfrac{113}{6}}+4-\dfrac{13}{18}-\left(\left(-\dfrac{113}{7}-\dfrac{18}{5}\right)-4\right)-\dfrac{147}{4}-\dfrac{263}{19}-20\\&=&-\dfrac{97}{5}-\dfrac{\dfrac{\dfrac{50}{3}\times-\dfrac{2141}{28}\times\left(-15\right)}{\dfrac{180}{7}}}{-\dfrac{113}{6}}+4-\dfrac{13}{18}-\left(\left(-\dfrac{113}{7}-\dfrac{18}{5}\right)-4\right)-\dfrac{147}{4}-\dfrac{263}{19}-20\\&=&-\dfrac{97}{5}-\dfrac{\dfrac{\dfrac{50}{3}\times-\dfrac{2141}{28}\times\left(-15\right)}{\dfrac{180}{7}}}{-\dfrac{113}{6}}+4-\dfrac{13}{18}-\left(-\dfrac{691}{35}-4\right)-\dfrac{147}{4}-\dfrac{263}{19}-20\\&=&-\dfrac{97}{5}-\dfrac{\dfrac{\left(-\dfrac{53525}{42}\right)\times\left(-15\right)}{\dfrac{180}{7}}}{-\dfrac{113}{6}}+4-\dfrac{13}{18}-\left(-\dfrac{691}{35}-4\right)-\dfrac{147}{4}-\dfrac{263}{19}-20\\&=&-\dfrac{97}{5}-\dfrac{\dfrac{\dfrac{267625}{14}}{\dfrac{180}{7}}}{-\dfrac{113}{6}}+4-\dfrac{13}{18}-\left(-\dfrac{691}{35}-4\right)-\dfrac{147}{4}-\dfrac{263}{19}-20\\&=&-\dfrac{97}{5}-\dfrac{\dfrac{\dfrac{267625}{14}}{\dfrac{180}{7}}}{-\dfrac{113}{6}}+4-\dfrac{13}{18}+\dfrac{831}{35}-\dfrac{147}{4}-\dfrac{263}{19}-20\\&=&-\dfrac{97}{5}-\dfrac{\dfrac{53525}{72}}{-\dfrac{113}{6}}+4-\dfrac{13}{18}+\dfrac{831}{35}-\dfrac{147}{4}-\dfrac{263}{19}-20\\&=&-\dfrac{97}{5}+\dfrac{53525}{1356}+4-\dfrac{13}{18}+\dfrac{831}{35}-\dfrac{147}{4}-\dfrac{263}{19}-20\\&=&-\dfrac{97}{5}+\dfrac{53525}{1356}+\dfrac{59}{18}+\dfrac{831}{35}-\dfrac{147}{4}-\dfrac{263}{19}-20\\&=&-\dfrac{97}{5}+\dfrac{53525}{1356}+\dfrac{17023}{630}-\dfrac{147}{4}-\dfrac{263}{19}-20\\&=&\dfrac{136093}{6780}+\dfrac{17023}{630}-\dfrac{147}{4}-\dfrac{263}{19}-20\\&=&\dfrac{136093}{6780}-\dfrac{12259}{1260}-\dfrac{263}{19}-20\\&=&\dfrac{136093}{6780}-\dfrac{564301}{23940}-20\\&=&-\dfrac{4732453}{1352610}-20\\&=&-\dfrac{31784653}{1352610}\\
\end{eqnarray*}