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e)
\(=28\left(\frac{3}{14}-\frac{13}{21}+\frac{29}{42}\right)-8=\frac{28.2}{7}-8=8-8=0\)
\(\frac37\) x (\(x\) - \(\frac{14}{9}\)) = - \(\frac{11}{7}\) x (\(x+\frac{14}{11}\))
\(\frac37x\) - \(\frac23\) = - \(\frac{11}{7}x\) - 2
\(\frac37\)\(x\) + \(\frac{11}{7}\)\(x\) = - 2 + \(\frac23\)
2\(x\) = \(-\frac43\)
\(x\) = - \(\frac43:2\)
\(x\) = - \(\frac23\)
Vậy \(x=-\frac23\)
73 x (\(x\) - \(\frac{14}{9}\)) = - \(\frac{11}{7}\) x (\(x + \frac{14}{11}\))
\(\frac{3}{7} x\) - \(\frac{2}{3}\) = - \(\frac{11}{7} x\) - 2
\(\frac{3}{7}\)\(x\) + \(\frac{11}{7}\)\(x\) = - 2 + \(\frac{2}{3}\)
2\(x\) = \(- \frac{4}{3}\)
\(x\) = - \(\frac{4}{3} : 2\)
\(x\) = - \(\frac{2}{3}\)
Vậy \(x = - \frac{2}{3}\)
e, \(\frac{3}{14}:\frac{1}{28}-\frac{13}{21}:\frac{1}{28}+\frac{28}{42}:\frac{1}{28}-8\)
\(=\left(\frac{3}{14}-\frac{13}{21}+\frac{2}{3}\right):\frac{1}{28}-8\)
\(=\frac{11}{42}:\frac{1}{28}-8\)
\(=\frac{22}{3}-8\)
\(=-\frac{2}{3}\)
e, \(\frac{3}{14}:\frac{1}{28}-\frac{13}{21}:\frac{1}{28}+\frac{28}{42}:\frac{1}{28}-8\)
\(=\left(\frac{3}{14}-\frac{13}{21}+\frac{2}{3}\right):\frac{1}{28}-8\)
\(=\frac{11}{42}:\frac{1}{28}-8\)
\(=\frac{22}{3}-8\)
\(=-\frac{2}{3}\)
\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)..........\left(1-\frac{1}{100}\right)\)
\(=\frac{1}{2}.\frac{2}{3}............\frac{99}{100}\)
\(=\frac{1.2.3.........99}{2.3...........100}\)
\(=\frac{1}{100}\)
Ta có: \(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{100}\right)\)
=\(\frac{1}{2}.\frac{2}{3}....\frac{99}{100}\)
=\(\frac{1.2....99}{2.3...100}\)
=\(\frac{1}{100}\)
linh vu mấu chốt để giải bài này là em phải biết phân tách số :
\(=\frac{-1}{10.9}-\frac{1}{9.8}-\frac{1}{8.7}-\frac{1}{7.6}-\frac{1}{6.5}-\frac{1}{5.4}-\frac{1}{4.3}-\frac{1}{3.2}-\frac{1}{2}\)
rồi đến đây trở về dạng cơ bản !
\(15\times\frac{1}{4}\times\frac{-5}{7}-25\times\frac{1}{4}\times\frac{-5}{7}\)
\(=\frac{1}{4}\times\frac{-5}{7}\left(15-25\right)\)
\(=\frac{1}{4}\times\frac{-5}{7}\times\left(-10\right)\)
\(=\frac{25}{14}\)
\(15\times\frac{1}{4}\times\frac{-5}{7}-25\times\frac{1}{4}\times\frac{-5}{7}=\frac{1}{4}\times\frac{-5}{7}\left(15-25\right)=\frac{1}{4}\times\frac{-5}{7}\times\left(-10\right)=\frac{25}{14}\)
\(=\frac{2.\left(\frac13+\frac17\right)}{-1-\frac{3.4}{28}+\frac{3}{28}}\)
\(=\frac{2.\left(\frac{7+3}{21}\right)-\frac{1}{14}}{-1-\frac{12}{28}+\frac{3}{28}}\)
\(=\frac{2.\frac{10}{21}-\frac{1}{14}}{\frac{-28}{28}-\frac{12}{28}+\frac{3}{28}}\)
\(=\frac{\frac{20}{21}-\frac{1}{14}}{\frac{-28-12+3}{28}}\)
\(=\frac{\frac{40}{42}-\frac{3}{42}}{\frac{-37}{28}}\)
\(=\frac{\frac{37}{42}}{-\frac{37}{28}}\)
\(=\frac{37}{42}.\frac{28}{-37}\)
\(=\frac{1}{42}.\frac{28}{-1}\)
\(=\frac{28}{-42}\)
\(=-\frac23\)