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#)Giải :
Đặt \(A=\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\)
\(A=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)
\(A=\frac{1}{5}-\frac{1}{10}\)
\(A=\frac{1}{10}\)
3/4 x 8/9 x 15/16 x ... x 99/100 x 120/121 = 3 x 8 x 15 x 99 x 120/ 4 x 9 x 16 x 100 x 121
= ( 1 x 3 ) x ( 2 x 4 ) x ( 3 x 5 ) x ... x ( 9 x 11 ) x ( 10 x 12 ) / ( 2 x 2 ) x ( 3 x 3 ) x ( 4 x 4 ) x ... x ( 10 x 10 ) x ( 11 x 11 )
= ( 1 x 2 x 3 x ... x 10 ) x ( 3 x 4 x 5 x ... x 12 ) / ( 2 x 3 x ... x 11 ) x ( 2 x 3 x ... x 11 ) = 12/11x2 = 6/11
\(\frac{22}{9}x-\frac{1}{3}=\frac{5}{9}\)
\(\Rightarrow\frac{22}{9}x=\frac{5}{9}+\frac{1}{3}\)
\(\Rightarrow\frac{22}{9}x=\frac{8}{9}\)
\(\Rightarrow x=\frac{8}{9}:\frac{22}{9}=\frac{8}{9}x\frac{9}{22}\)
\(\Rightarrow x=\frac{4}{11}\)
\(\frac{22}{9}x-\frac{1}{3}=\frac{5}{9}\)
\(\frac{22}{9}x=\frac{5}{9}+\frac{1}{3}\)
\(\frac{22}{9}x=\frac{8}{9}\)
\(x=\frac{8}{9}:\frac{22}{9}=\frac{4}{11}\)
vậy \(x=\frac{4}{11}\)
\(\frac{1}{3}\) + \(\frac{5}{6}\): \(\left(x-2\frac{1}{5}\right)\)= \(\frac{3}{4}\)
<=> \(\frac{5}{6}\):\(\left(x-2\frac{1}{5}\right)\)= \(\frac{3}{4}\)- \(\frac{1}{3}\)
<=> \(\frac{5}{6}\) : \(\left(x-2\frac{1}{5}\right)\) = \(\frac{5}{12}\)
<=> \(\left(x-2\frac{1}{5}\right)\) = \(\frac{5}{6}\) : \(\frac{5}{12}\)
,<=> \(\left(x-2\frac{1}{5}\right)\)= 2
<=. x = 2 + \(\frac{11}{5}\)
<=> x = \(\frac{21}{5}\)
Mk cần gấp
\(\frac{22}{9}-x.\frac{1}{3}=\frac{5}{9}\)
\(\Rightarrow\frac{22}{9}-\frac{x}{3}=\frac{5}{9}\)
\(\Rightarrow\frac{x}{3}=\frac{22}{9}-\frac{5}{9}\)
\(\Rightarrow\frac{x}{3}=\frac{17}{9}\)
\(\Rightarrow\frac{3.x}{9}=\frac{17}{9}\Rightarrow3.x=17\Rightarrow x=\frac{17}{3}\)
Chúc bn hc giỏi!