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-5.(x+1/5) -1/2.(x-2/3)=3/2x-5/6
-5x + (-1) -1/2x -1/3=3/2x-5/6
-5x-1/2x-3/2x=1+1/3-5/6
x.(-5-1/2-3/2)= 6/6+2/6+(-5/6)
x.(-10/2+(-1/2)+(-3/2))=3/6
x.6/2=1/2
x=1/2:6/2
x=1/6
Vậy x = 1/6
\(\frac{x-1}{21}=\frac{3}{x+1}\)
=> \(\left(x-1\right)\left(x+1\right)=21\cdot3\)
=> \(x^2-1=63\)
=> \(x^2=64\)
=> \(\orbr{\begin{cases}x^2=8^2\\x^2=\left(-8\right)^2\end{cases}\Rightarrow}\orbr{\begin{cases}x=8\\x=-8\end{cases}}\)
\(2\frac{7}{9}-\frac{12}{13}x=\frac{7}{9}\)
=> \(\frac{12}{13}x=2\)
=> \(x=\frac{13}{6}\)
d, \(\frac{x-1}{21}=\frac{3}{x+1}\)
\(\Leftrightarrow\left(x-1\right)\left(x+1\right)=63\)
\(\Leftrightarrow x^2-1=63\Leftrightarrow x^2=64\Leftrightarrow x=\pm8\)
e, \(2\frac{7}{9}-\frac{12}{13}x=\frac{7}{9}\)
\(\Leftrightarrow\frac{12}{13}x=2\Leftrightarrow x=\frac{13}{6}\)
\(\frac{1}{2}\left(x+1\right):\frac{3}{7}=\frac{32}{135}\)
\(\frac{1}{2}\left(x+1\right)=\frac{32}{135}.\frac{3}{7}\)
\(\frac{1}{2}\left(x+1\right)=\frac{32}{315}\)
\(x+1=\frac{32}{315}:\frac{1}{2}\)
\(x+1=\frac{64}{315}\)
\(x=\frac{64}{315}-1=-\frac{251}{315}\)
\(\frac{2}{6}+\frac{2}{12}+...+\frac{2}{x.\left(x+1\right)}=\frac{2011}{2013}\)
\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2011}{2013}:2\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{2011}{4026}\)
\(\frac{\left(x+1-2\right)}{2.\left(x+1\right)}=\frac{2011}{4026}\)