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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 \[\dfrac{\dfrac{\dfrac{\left(-10-12+\dfrac{61}{4}\right)+10-\dfrac{\dfrac{0}{\dfrac{69}{7}}}{\dfrac{59}{8}}+\dfrac{61}{4}}{\dfrac{\dfrac{\dfrac{-10}{\dfrac{-\dfrac{15}{4}}{9}}}{-10}}{-10}}}{\dfrac{92}{7}-\dfrac{\dfrac{\dfrac{59}{8}}{-9}}{\dfrac{69}{7}}}}{12}\times\left(\left(\left(-9+12-9-\dfrac{61}{4}\right)-2\right)-\dfrac{\dfrac{12-9}{\dfrac{92}{7}\times12\times\left(-\dfrac{33}{2}\right)}}{-10}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times\left(\dfrac{69}{7}-\dfrac{61}{4}\right)\times\left(-10\right)\times12\right)+10\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=\dfrac{\dfrac{\dfrac{\left(-10-12+\dfrac{61}{4}\right)+10-\dfrac{\dfrac{0}{\dfrac{69}{7}}}{\dfrac{59}{8}}+\dfrac{61}{4}}{\dfrac{\dfrac{\dfrac{-10}{\dfrac{-\dfrac{15}{4}}{9}}}{-10}}{-10}}}{\dfrac{92}{7}-\dfrac{\dfrac{\dfrac{59}{8}}{-9}}{\dfrac{69}{7}}}}{12}\times\left(\left(\left(-9+12-9-\dfrac{61}{4}\right)-2\right)-\dfrac{\dfrac{12-9}{\dfrac{92}{7}\times12\times\left(-\dfrac{33}{2}\right)}}{-10}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times\left(\dfrac{69}{7}-\dfrac{61}{4}\right)\times\left(-10\right)\times12\right)+10=\dfrac{4849276556114430}{232481578560}\) . Voici le détail : \begin{eqnarray*} X &=&\dfrac{\dfrac{\dfrac{\left(-22+\dfrac{61}{4}\right)+10-\dfrac{\dfrac{0}{\dfrac{69}{7}}}{\dfrac{59}{8}}+\dfrac{61}{4}}{\dfrac{\dfrac{\dfrac{-10}{\dfrac{-\dfrac{15}{4}}{9}}}{-10}}{-10}}}{\dfrac{92}{7}-\dfrac{\dfrac{\dfrac{59}{8}}{-9}}{\dfrac{69}{7}}}}{12}\times\left(\left(\left(-9+12-9-\dfrac{61}{4}\right)-2\right)-\dfrac{\dfrac{12-9}{\dfrac{92}{7}\times12\times\left(-\dfrac{33}{2}\right)}}{-10}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times\left(\dfrac{69}{7}-\dfrac{61}{4}\right)\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{27}{4}+10-\dfrac{\dfrac{0}{\dfrac{69}{7}}}{\dfrac{59}{8}}+\dfrac{61}{4}}{\dfrac{\dfrac{\dfrac{-10}{\dfrac{-\dfrac{15}{4}}{9}}}{-10}}{-10}}}{\dfrac{92}{7}-\dfrac{\dfrac{\dfrac{59}{8}}{-9}}{\dfrac{69}{7}}}}{12}\times\left(\left(\left(-9+12-9-\dfrac{61}{4}\right)-2\right)-\dfrac{\dfrac{12-9}{\dfrac{92}{7}\times12\times\left(-\dfrac{33}{2}\right)}}{-10}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times\left(\dfrac{69}{7}-\dfrac{61}{4}\right)\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{27}{4}+10-\dfrac{0}{\dfrac{59}{8}}+\dfrac{61}{4}}{\dfrac{\dfrac{\dfrac{-10}{\dfrac{-\dfrac{15}{4}}{9}}}{-10}}{-10}}}{\dfrac{92}{7}-\dfrac{\dfrac{\dfrac{59}{8}}{-9}}{\dfrac{69}{7}}}}{12}\times\left(\left(\left(-9+12-9-\dfrac{61}{4}\right)-2\right)-\dfrac{\dfrac{12-9}{\dfrac{92}{7}\times12\times\left(-\dfrac{33}{2}\right)}}{-10}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times\left(\dfrac{69}{7}-\dfrac{61}{4}\right)\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{27}{4}+10-0+\dfrac{61}{4}}{\dfrac{\dfrac{\dfrac{-10}{\dfrac{-\dfrac{15}{4}}{9}}}{-10}}{-10}}}{\dfrac{92}{7}-\dfrac{\dfrac{\dfrac{59}{8}}{-9}}{\dfrac{69}{7}}}}{12}\times\left(\left(\left(-9+12-9-\dfrac{61}{4}\right)-2\right)-\dfrac{\dfrac{12-9}{\dfrac{92}{7}\times12\times\left(-\dfrac{33}{2}\right)}}{-10}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times\left(\dfrac{69}{7}-\dfrac{61}{4}\right)\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{27}{4}+10-0+\dfrac{61}{4}}{\dfrac{\dfrac{\dfrac{-10}{-\dfrac{5}{12}}}{-10}}{-10}}}{\dfrac{92}{7}-\dfrac{\dfrac{\dfrac{59}{8}}{-9}}{\dfrac{69}{7}}}}{12}\times\left(\left(\left(-9+12-9-\dfrac{61}{4}\right)-2\right)-\dfrac{\dfrac{12-9}{\dfrac{92}{7}\times12\times\left(-\dfrac{33}{2}\right)}}{-10}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times\left(\dfrac{69}{7}-\dfrac{61}{4}\right)\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{27}{4}+10-0+\dfrac{61}{4}}{\dfrac{\dfrac{\dfrac{-10}{-\dfrac{5}{12}}}{-10}}{-10}}}{\dfrac{92}{7}-\dfrac{-\dfrac{59}{72}}{\dfrac{69}{7}}}}{12}\times\left(\left(\left(-9+12-9-\dfrac{61}{4}\right)-2\right)-\dfrac{\dfrac{12-9}{\dfrac{92}{7}\times12\times\left(-\dfrac{33}{2}\right)}}{-10}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times\left(\dfrac{69}{7}-\dfrac{61}{4}\right)\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{27}{4}+10-0+\dfrac{61}{4}}{\dfrac{\dfrac{\dfrac{-10}{-\dfrac{5}{12}}}{-10}}{-10}}}{\dfrac{92}{7}+\dfrac{413}{4968}}}{12}\times\left(\left(\left(-9+12-9-\dfrac{61}{4}\right)-2\right)-\dfrac{\dfrac{12-9}{\dfrac{92}{7}\times12\times\left(-\dfrac{33}{2}\right)}}{-10}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times\left(\dfrac{69}{7}-\dfrac{61}{4}\right)\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{27}{4}+10-0+\dfrac{61}{4}}{\dfrac{\dfrac{\dfrac{-10}{-\dfrac{5}{12}}}{-10}}{-10}}}{\dfrac{92}{7}+\dfrac{413}{4968}}}{12}\times\left(\left(\left(3-9-\dfrac{61}{4}\right)-2\right)-\dfrac{\dfrac{12-9}{\dfrac{92}{7}\times12\times\left(-\dfrac{33}{2}\right)}}{-10}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times\left(\dfrac{69}{7}-\dfrac{61}{4}\right)\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{27}{4}+10-0+\dfrac{61}{4}}{\dfrac{\dfrac{\dfrac{-10}{-\dfrac{5}{12}}}{-10}}{-10}}}{\dfrac{92}{7}+\dfrac{413}{4968}}}{12}\times\left(\left(\left(-6-\dfrac{61}{4}\right)-2\right)-\dfrac{\dfrac{12-9}{\dfrac{92}{7}\times12\times\left(-\dfrac{33}{2}\right)}}{-10}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times\left(\dfrac{69}{7}-\dfrac{61}{4}\right)\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{27}{4}+10-0+\dfrac{61}{4}}{\dfrac{\dfrac{\dfrac{-10}{-\dfrac{5}{12}}}{-10}}{-10}}}{\dfrac{92}{7}+\dfrac{413}{4968}}}{12}\times\left(\left(-\dfrac{85}{4}-2\right)-\dfrac{\dfrac{12-9}{\dfrac{92}{7}\times12\times\left(-\dfrac{33}{2}\right)}}{-10}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times\left(\dfrac{69}{7}-\dfrac{61}{4}\right)\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{27}{4}+10-0+\dfrac{61}{4}}{\dfrac{\dfrac{\dfrac{-10}{-\dfrac{5}{12}}}{-10}}{-10}}}{\dfrac{92}{7}+\dfrac{413}{4968}}}{12}\times\left(\left(-\dfrac{85}{4}-2\right)-\dfrac{\dfrac{3}{\dfrac{92}{7}\times12\times\left(-\dfrac{33}{2}\right)}}{-10}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times\left(\dfrac{69}{7}-\dfrac{61}{4}\right)\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{27}{4}+10-0+\dfrac{61}{4}}{\dfrac{\dfrac{\dfrac{-10}{-\dfrac{5}{12}}}{-10}}{-10}}}{\dfrac{92}{7}+\dfrac{413}{4968}}}{12}\times\left(\left(-\dfrac{85}{4}-2\right)-\dfrac{\dfrac{3}{\dfrac{1104}{7}\times\left(-\dfrac{33}{2}\right)}}{-10}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times\left(\dfrac{69}{7}-\dfrac{61}{4}\right)\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{27}{4}+10-0+\dfrac{61}{4}}{\dfrac{\dfrac{\dfrac{-10}{-\dfrac{5}{12}}}{-10}}{-10}}}{\dfrac{92}{7}+\dfrac{413}{4968}}}{12}\times\left(\left(-\dfrac{85}{4}-2\right)-\dfrac{\dfrac{3}{-\dfrac{18216}{7}}}{-10}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times\left(\dfrac{69}{7}-\dfrac{61}{4}\right)\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{-\dfrac{27}{4}+10-0+\dfrac{61}{4}}{\dfrac{\dfrac{\dfrac{-10}{-\dfrac{5}{12}}}{-10}}{-10}}}{\dfrac{92}{7}+\dfrac{413}{4968}}}{12}\times\left(\left(-\dfrac{85}{4}-2\right)-\dfrac{\dfrac{3}{-\dfrac{18216}{7}}}{-10}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times-\dfrac{151}{28}\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{\dfrac{13}{4}-0+\dfrac{61}{4}}{\dfrac{\dfrac{\dfrac{-10}{-\dfrac{5}{12}}}{-10}}{-10}}}{\dfrac{92}{7}+\dfrac{413}{4968}}}{12}\times\left(\left(-\dfrac{85}{4}-2\right)-\dfrac{\dfrac{3}{-\dfrac{18216}{7}}}{-10}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times-\dfrac{151}{28}\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{\dfrac{13}{4}+\dfrac{61}{4}}{\dfrac{\dfrac{\dfrac{-10}{-\dfrac{5}{12}}}{-10}}{-10}}}{\dfrac{92}{7}+\dfrac{413}{4968}}}{12}\times\left(\left(-\dfrac{85}{4}-2\right)-\dfrac{\dfrac{3}{-\dfrac{18216}{7}}}{-10}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times-\dfrac{151}{28}\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{\dfrac{37}{2}}{\dfrac{\dfrac{\dfrac{-10}{-\dfrac{5}{12}}}{-10}}{-10}}}{\dfrac{92}{7}+\dfrac{413}{4968}}}{12}\times\left(\left(-\dfrac{85}{4}-2\right)-\dfrac{\dfrac{3}{-\dfrac{18216}{7}}}{-10}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times-\dfrac{151}{28}\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{\dfrac{37}{2}}{\dfrac{\dfrac{24}{-10}}{-10}}}{\dfrac{92}{7}+\dfrac{413}{4968}}}{12}\times\left(\left(-\dfrac{85}{4}-2\right)-\dfrac{\dfrac{3}{-\dfrac{18216}{7}}}{-10}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times-\dfrac{151}{28}\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{\dfrac{37}{2}}{\dfrac{-\dfrac{12}{5}}{-10}}}{\dfrac{92}{7}+\dfrac{413}{4968}}}{12}\times\left(\left(-\dfrac{85}{4}-2\right)-\dfrac{\dfrac{3}{-\dfrac{18216}{7}}}{-10}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times-\dfrac{151}{28}\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{\dfrac{37}{2}}{\dfrac{6}{25}}}{\dfrac{92}{7}+\dfrac{413}{4968}}}{12}\times\left(\left(-\dfrac{85}{4}-2\right)-\dfrac{\dfrac{3}{-\dfrac{18216}{7}}}{-10}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times-\dfrac{151}{28}\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{\dfrac{37}{2}}{\dfrac{6}{25}}}{\dfrac{459947}{34776}}}{12}\times\left(\left(-\dfrac{85}{4}-2\right)-\dfrac{\dfrac{3}{-\dfrac{18216}{7}}}{-10}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times-\dfrac{151}{28}\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{\dfrac{37}{2}}{\dfrac{6}{25}}}{\dfrac{459947}{34776}}}{12}\times\left(-\dfrac{93}{4}-\dfrac{\dfrac{3}{-\dfrac{18216}{7}}}{-10}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times-\dfrac{151}{28}\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{\dfrac{37}{2}}{\dfrac{6}{25}}}{\dfrac{459947}{34776}}}{12}\times\left(-\dfrac{93}{4}-\dfrac{-\dfrac{7}{6072}}{-10}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times-\dfrac{151}{28}\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{\dfrac{37}{2}}{\dfrac{6}{25}}}{\dfrac{459947}{34776}}}{12}\times\left(-\dfrac{93}{4}-\dfrac{7}{60720}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{70}{11}-\dfrac{15}{4}-11-11\right)\times-\dfrac{151}{28}\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{\dfrac{37}{2}}{\dfrac{6}{25}}}{\dfrac{459947}{34776}}}{12}\times\left(-\dfrac{93}{4}-\dfrac{7}{60720}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{445}{44}-11-11\right)\times-\dfrac{151}{28}\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{\dfrac{37}{2}}{\dfrac{6}{25}}}{\dfrac{459947}{34776}}}{12}\times\left(-\dfrac{93}{4}-\dfrac{7}{60720}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}+\left(-\dfrac{929}{44}-11\right)\times-\dfrac{151}{28}\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{\dfrac{37}{2}}{\dfrac{6}{25}}}{\dfrac{459947}{34776}}}{12}\times\left(-\dfrac{93}{4}-\dfrac{7}{60720}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}-\dfrac{1413}{44}\times-\dfrac{151}{28}\times\left(-10\right)\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{\dfrac{37}{2}}{\dfrac{6}{25}}}{\dfrac{459947}{34776}}}{12}\times\left(-\dfrac{93}{4}-\dfrac{7}{60720}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}-\dfrac{1413}{44}\times\dfrac{755}{14}\times12\right)+10\\&=&\dfrac{\dfrac{\dfrac{925}{12}}{\dfrac{459947}{34776}}}{12}\times\left(-\dfrac{93}{4}-\dfrac{7}{60720}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}-\dfrac{1413}{44}\times\dfrac{755}{14}\times12\right)+10\\&=&\dfrac{\dfrac{72450}{12431}}{12}\times\left(-\dfrac{93}{4}-\dfrac{7}{60720}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}-\dfrac{1413}{44}\times\dfrac{755}{14}\times12\right)+10\\&=&\dfrac{12075}{24862}\times\left(-\dfrac{93}{4}-\dfrac{7}{60720}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}-\dfrac{1413}{44}\times\dfrac{755}{14}\times12\right)+10\\&=&\dfrac{12075}{24862}\times\left(-\dfrac{1411747}{60720}+10\right)\times\left(-11\right)+9-\left(\dfrac{92}{7}-\dfrac{1413}{44}\times\dfrac{755}{14}\times12\right)+10\\&=&\dfrac{12075}{24862}\times-\dfrac{804547}{60720}\times\left(-11\right)+9-\left(\dfrac{92}{7}-\dfrac{1413}{44}\times\dfrac{755}{14}\times12\right)+10\\&=&\dfrac{12075}{24862}\times-\dfrac{804547}{60720}\times\left(-11\right)+9-\left(\dfrac{92}{7}-\dfrac{1066815}{616}\times12\right)+10\\&=&\dfrac{12075}{24862}\times-\dfrac{804547}{60720}\times\left(-11\right)+9-\left(\dfrac{92}{7}-\dfrac{3200445}{154}\right)+10\\&=&-\dfrac{9714905025}{1509620640}\times\left(-11\right)+9-\left(\dfrac{92}{7}-\dfrac{3200445}{154}\right)+10\\&=&\dfrac{106863955275}{1509620640}+9-\left(\dfrac{92}{7}-\dfrac{3200445}{154}\right)+10\\&=&\dfrac{106863955275}{1509620640}+9+\dfrac{3198421}{154}+10\\&=&\dfrac{120450541035}{1509620640}+\dfrac{3198421}{154}+10\\&=&\dfrac{4846951740328830}{232481578560}+10\\&=&\dfrac{4849276556114430}{232481578560}\\ \end{eqnarray*}