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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 \[\left(-\dfrac{56}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{56}{3}+\dfrac{91}{9}}{8}}{8}}{\dfrac{\dfrac{6}{6}}{6+2+4}}\times\left(-\dfrac{67}{2}\right)+\dfrac{\dfrac{6}{-4+4-\dfrac{43}{10}-4}}{-2}+\left(\dfrac{\dfrac{70}{11}}{4}-4+\left(-\dfrac{134}{7}\right)\times\left(-1\right)\times\left(-4\right)\right)-\left(6-\dfrac{70}{11}\right)\times\left(-4\right)\times\left(-\dfrac{91}{9}+8-\dfrac{49}{6}\right)-\left(\dfrac{70}{11}-\dfrac{134}{7}+6\right)\]
Cliquer ici pour afficher la solution

Exercice


On a \( X=\left(-\dfrac{56}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{56}{3}+\dfrac{91}{9}}{8}}{8}}{\dfrac{\dfrac{6}{6}}{6+2+4}}\times\left(-\dfrac{67}{2}\right)+\dfrac{\dfrac{6}{-4+4-\dfrac{43}{10}-4}}{-2}+\left(\dfrac{\dfrac{70}{11}}{4}-4+\left(-\dfrac{134}{7}\right)\times\left(-1\right)\times\left(-4\right)\right)-\left(6-\dfrac{70}{11}\right)\times\left(-4\right)\times\left(-\dfrac{91}{9}+8-\dfrac{49}{6}\right)-\left(\dfrac{70}{11}-\dfrac{134}{7}+6\right)=-\dfrac{4389971202}{4141368}\) . Voici le détail : \begin{eqnarray*} X &=&\left(-\dfrac{56}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{77}{9}}{8}}{8}}{\dfrac{\dfrac{6}{6}}{6+2+4}}\times\left(-\dfrac{67}{2}\right)+\dfrac{\dfrac{6}{-4+4-\dfrac{43}{10}-4}}{-2}+\left(\dfrac{\dfrac{70}{11}}{4}-4+\left(-\dfrac{134}{7}\right)\times\left(-1\right)\times\left(-4\right)\right)-\left(6-\dfrac{70}{11}\right)\times\left(-4\right)\times\left(-\dfrac{91}{9}+8-\dfrac{49}{6}\right)-\left(\dfrac{70}{11}-\dfrac{134}{7}+6\right)\\&=&\left(-\dfrac{56}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{77}{9}}{8}}{8}}{\dfrac{\dfrac{6}{6}}{8+4}}\times\left(-\dfrac{67}{2}\right)+\dfrac{\dfrac{6}{-4+4-\dfrac{43}{10}-4}}{-2}+\left(\dfrac{\dfrac{70}{11}}{4}-4+\left(-\dfrac{134}{7}\right)\times\left(-1\right)\times\left(-4\right)\right)-\left(6-\dfrac{70}{11}\right)\times\left(-4\right)\times\left(-\dfrac{91}{9}+8-\dfrac{49}{6}\right)-\left(\dfrac{70}{11}-\dfrac{134}{7}+6\right)\\&=&\left(-\dfrac{56}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{77}{9}}{8}}{8}}{\dfrac{\dfrac{6}{6}}{12}}\times\left(-\dfrac{67}{2}\right)+\dfrac{\dfrac{6}{-4+4-\dfrac{43}{10}-4}}{-2}+\left(\dfrac{\dfrac{70}{11}}{4}-4+\left(-\dfrac{134}{7}\right)\times\left(-1\right)\times\left(-4\right)\right)-\left(6-\dfrac{70}{11}\right)\times\left(-4\right)\times\left(-\dfrac{91}{9}+8-\dfrac{49}{6}\right)-\left(\dfrac{70}{11}-\dfrac{134}{7}+6\right)\\&=&\left(-\dfrac{56}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{77}{9}}{8}}{8}}{\dfrac{\dfrac{6}{6}}{12}}\times\left(-\dfrac{67}{2}\right)+\dfrac{\dfrac{6}{-4-\dfrac{3}{10}-4}}{-2}+\left(\dfrac{\dfrac{70}{11}}{4}-4+\left(-\dfrac{134}{7}\right)\times\left(-1\right)\times\left(-4\right)\right)-\left(6-\dfrac{70}{11}\right)\times\left(-4\right)\times\left(-\dfrac{91}{9}+8-\dfrac{49}{6}\right)-\left(\dfrac{70}{11}-\dfrac{134}{7}+6\right)\\&=&\left(-\dfrac{56}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{77}{9}}{8}}{8}}{\dfrac{\dfrac{6}{6}}{12}}\times\left(-\dfrac{67}{2}\right)+\dfrac{\dfrac{6}{-4-\dfrac{3}{10}-4}}{-2}+\left(\dfrac{35}{22}-4+\left(-\dfrac{134}{7}\right)\times\left(-1\right)\times\left(-4\right)\right)-\left(6-\dfrac{70}{11}\right)\times\left(-4\right)\times\left(-\dfrac{91}{9}+8-\dfrac{49}{6}\right)-\left(\dfrac{70}{11}-\dfrac{134}{7}+6\right)\\&=&\left(-\dfrac{56}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{77}{9}}{8}}{8}}{\dfrac{\dfrac{6}{6}}{12}}\times\left(-\dfrac{67}{2}\right)+\dfrac{\dfrac{6}{-4-\dfrac{3}{10}-4}}{-2}+\left(\dfrac{35}{22}-4+\dfrac{134}{7}\times\left(-4\right)\right)-\left(6-\dfrac{70}{11}\right)\times\left(-4\right)\times\left(-\dfrac{91}{9}+8-\dfrac{49}{6}\right)-\left(\dfrac{70}{11}-\dfrac{134}{7}+6\right)\\&=&\left(-\dfrac{56}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{77}{9}}{8}}{8}}{\dfrac{\dfrac{6}{6}}{12}}\times\left(-\dfrac{67}{2}\right)+\dfrac{\dfrac{6}{-4-\dfrac{3}{10}-4}}{-2}+\left(\dfrac{35}{22}-4-\dfrac{536}{7}\right)-\left(6-\dfrac{70}{11}\right)\times\left(-4\right)\times\left(-\dfrac{91}{9}+8-\dfrac{49}{6}\right)-\left(\dfrac{70}{11}-\dfrac{134}{7}+6\right)\\&=&\left(-\dfrac{56}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{77}{9}}{8}}{8}}{\dfrac{\dfrac{6}{6}}{12}}\times\left(-\dfrac{67}{2}\right)+\dfrac{\dfrac{6}{-4-\dfrac{3}{10}-4}}{-2}+\left(\dfrac{35}{22}-4-\dfrac{536}{7}\right)+\dfrac{4}{11}\times\left(-4\right)\times\left(-\dfrac{91}{9}+8-\dfrac{49}{6}\right)-\left(\dfrac{70}{11}-\dfrac{134}{7}+6\right)\\&=&\left(-\dfrac{56}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{77}{9}}{8}}{8}}{\dfrac{\dfrac{6}{6}}{12}}\times\left(-\dfrac{67}{2}\right)+\dfrac{\dfrac{6}{-4-\dfrac{3}{10}-4}}{-2}+\left(\dfrac{35}{22}-4-\dfrac{536}{7}\right)+\dfrac{4}{11}\times\left(-4\right)\times\left(-\dfrac{19}{9}-\dfrac{49}{6}\right)-\left(\dfrac{70}{11}-\dfrac{134}{7}+6\right)\\&=&\left(-\dfrac{56}{3}\right)\times\dfrac{\dfrac{\dfrac{-\dfrac{77}{9}}{8}}{8}}{\dfrac{\dfrac{6}{6}}{12}}\times\left(-\dfrac{67}{2}\right)+\dfrac{\dfrac{6}{-4-\dfrac{3}{10}-4}}{-2}+\left(\dfrac{35}{22}-4-\dfrac{536}{7}\right)+\dfrac{4}{11}\times\left(-4\right)\times\left(-\dfrac{185}{18}\right)-\left(\dfrac{70}{11}-\dfrac{134}{7}+6\right)\\&=&\left(-\dfrac{56}{3}\right)\times\dfrac{\dfrac{-\dfrac{77}{72}}{8}}{\dfrac{\dfrac{6}{6}}{12}}\times\left(-\dfrac{67}{2}\right)+\dfrac{\dfrac{6}{-4-\dfrac{3}{10}-4}}{-2}+\left(\dfrac{35}{22}-4-\dfrac{536}{7}\right)+\dfrac{4}{11}\times\left(-4\right)\times\left(-\dfrac{185}{18}\right)-\left(\dfrac{70}{11}-\dfrac{134}{7}+6\right)\\&=&\left(-\dfrac{56}{3}\right)\times\dfrac{-\dfrac{77}{576}}{\dfrac{\dfrac{6}{6}}{12}}\times\left(-\dfrac{67}{2}\right)+\dfrac{\dfrac{6}{-4-\dfrac{3}{10}-4}}{-2}+\left(\dfrac{35}{22}-4-\dfrac{536}{7}\right)+\dfrac{4}{11}\times\left(-4\right)\times\left(-\dfrac{185}{18}\right)-\left(\dfrac{70}{11}-\dfrac{134}{7}+6\right)\\&=&\left(-\dfrac{56}{3}\right)\times\dfrac{-\dfrac{77}{576}}{\dfrac{1}{12}}\times\left(-\dfrac{67}{2}\right)+\dfrac{\dfrac{6}{-4-\dfrac{3}{10}-4}}{-2}+\left(\dfrac{35}{22}-4-\dfrac{536}{7}\right)+\dfrac{4}{11}\times\left(-4\right)\times\left(-\dfrac{185}{18}\right)-\left(\dfrac{70}{11}-\dfrac{134}{7}+6\right)\\&=&\left(-\dfrac{56}{3}\right)\times\dfrac{-\dfrac{77}{576}}{\dfrac{1}{12}}\times\left(-\dfrac{67}{2}\right)+\dfrac{\dfrac{6}{-4-\dfrac{3}{10}-4}}{-2}+\left(\dfrac{35}{22}-4-\dfrac{536}{7}\right)+\dfrac{4}{11}\times\left(-4\right)\times\left(-\dfrac{185}{18}\right)-\left(\dfrac{70}{11}-\dfrac{134}{7}+6\right)\\&=&\left(-\dfrac{56}{3}\right)\times\dfrac{-\dfrac{77}{576}}{\dfrac{1}{12}}\times\left(-\dfrac{67}{2}\right)+\dfrac{\dfrac{6}{-\dfrac{43}{10}-4}}{-2}+\left(\dfrac{35}{22}-4-\dfrac{536}{7}\right)+\dfrac{4}{11}\times\left(-4\right)\times\left(-\dfrac{185}{18}\right)-\left(\dfrac{70}{11}-\dfrac{134}{7}+6\right)\\&=&\left(-\dfrac{56}{3}\right)\times\dfrac{-\dfrac{77}{576}}{\dfrac{1}{12}}\times\left(-\dfrac{67}{2}\right)+\dfrac{\dfrac{6}{-\dfrac{83}{10}}}{-2}+\left(\dfrac{35}{22}-4-\dfrac{536}{7}\right)+\dfrac{4}{11}\times\left(-4\right)\times\left(-\dfrac{185}{18}\right)-\left(\dfrac{70}{11}-\dfrac{134}{7}+6\right)\\&=&\left(-\dfrac{56}{3}\right)\times\dfrac{-\dfrac{77}{576}}{\dfrac{1}{12}}\times\left(-\dfrac{67}{2}\right)+\dfrac{\dfrac{6}{-\dfrac{83}{10}}}{-2}+\left(-\dfrac{53}{22}-\dfrac{536}{7}\right)+\dfrac{4}{11}\times\left(-4\right)\times\left(-\dfrac{185}{18}\right)-\left(\dfrac{70}{11}-\dfrac{134}{7}+6\right)\\&=&\left(-\dfrac{56}{3}\right)\times\dfrac{-\dfrac{77}{576}}{\dfrac{1}{12}}\times\left(-\dfrac{67}{2}\right)+\dfrac{\dfrac{6}{-\dfrac{83}{10}}}{-2}-\dfrac{12163}{154}+\dfrac{4}{11}\times\left(-4\right)\times\left(-\dfrac{185}{18}\right)-\left(\dfrac{70}{11}-\dfrac{134}{7}+6\right)\\&=&\left(-\dfrac{56}{3}\right)\times\dfrac{-\dfrac{77}{576}}{\dfrac{1}{12}}\times\left(-\dfrac{67}{2}\right)+\dfrac{\dfrac{6}{-\dfrac{83}{10}}}{-2}-\dfrac{12163}{154}-\left(\dfrac{16}{11}\right)\times\left(-\dfrac{185}{18}\right)-\left(\dfrac{70}{11}-\dfrac{134}{7}+6\right)\\&=&\left(-\dfrac{56}{3}\right)\times\dfrac{-\dfrac{77}{576}}{\dfrac{1}{12}}\times\left(-\dfrac{67}{2}\right)+\dfrac{\dfrac{6}{-\dfrac{83}{10}}}{-2}-\dfrac{12163}{154}+\dfrac{1480}{99}-\left(\dfrac{70}{11}-\dfrac{134}{7}+6\right)\\&=&\left(-\dfrac{56}{3}\right)\times\dfrac{-\dfrac{77}{576}}{\dfrac{1}{12}}\times\left(-\dfrac{67}{2}\right)+\dfrac{\dfrac{6}{-\dfrac{83}{10}}}{-2}-\dfrac{12163}{154}+\dfrac{1480}{99}-\left(-\dfrac{984}{77}+6\right)\\&=&\left(-\dfrac{56}{3}\right)\times\dfrac{-\dfrac{77}{576}}{\dfrac{1}{12}}\times\left(-\dfrac{67}{2}\right)+\dfrac{\dfrac{6}{-\dfrac{83}{10}}}{-2}-\dfrac{12163}{154}+\dfrac{1480}{99}+\dfrac{522}{77}\\&=&\left(-\dfrac{56}{3}\right)\times\left(-\dfrac{77}{48}\right)\times\left(-\dfrac{67}{2}\right)+\dfrac{\dfrac{6}{-\dfrac{83}{10}}}{-2}-\dfrac{12163}{154}+\dfrac{1480}{99}+\dfrac{522}{77}\\&=&\left(-\dfrac{56}{3}\right)\times\left(-\dfrac{77}{48}\right)\times\left(-\dfrac{67}{2}\right)+\dfrac{-\dfrac{60}{83}}{-2}-\dfrac{12163}{154}+\dfrac{1480}{99}+\dfrac{522}{77}\\&=&\left(-\dfrac{56}{3}\right)\times\left(-\dfrac{77}{48}\right)\times\left(-\dfrac{67}{2}\right)+\dfrac{30}{83}-\dfrac{12163}{154}+\dfrac{1480}{99}+\dfrac{522}{77}\\&=&\left(-\dfrac{56}{3}\right)\times\left(-\dfrac{77}{48}\right)\times\left(-\dfrac{67}{2}\right)+\dfrac{30}{83}-\dfrac{88747}{1386}+\dfrac{522}{77}\\&=&\left(-\dfrac{56}{3}\right)\times\left(-\dfrac{77}{48}\right)\times\left(-\dfrac{67}{2}\right)+\dfrac{30}{83}-\dfrac{79351}{1386}\\&=&\dfrac{539}{18}\times\left(-\dfrac{67}{2}\right)+\dfrac{30}{83}-\dfrac{79351}{1386}\\&=&-\dfrac{36113}{36}+\dfrac{30}{83}-\dfrac{79351}{1386}\\&=&-\dfrac{36113}{36}-\dfrac{6544553}{115038}\\&=&-\dfrac{4389971202}{4141368}\\ \end{eqnarray*}