\(2n-1⋮3n+2\)
\(\Rightarrow3.\left(2n-1\right)⋮3n+2\)
\(\Rightarrow2.\left(3n+2\right)-7⋮3n+2\)
\(\Rightarrow7⋮3n+2\)
\(\Rightarrow3n+2\inƯ\left(7\right)=\left\{-1,1,-7,7\right\}\)
\(\Rightarrow n\in\left\{-1,-\dfrac{1}{3},-3,\dfrac{5}{3}\right\}\)
Mà \(n\in Z\Rightarrow n\in\left\{-1,-3\right\}\)
\(2n-1⋮3n+2\)
\(\Leftrightarrow\left(2n-1\right)-\left(3n+2\right)⋮3n+2\)
\(\Leftrightarrow n+3⋮3n+2\)
\(\Leftrightarrow\left(3n+9\right)-\left(3n+2\right)⋮3n+2\)
\(\Leftrightarrow7⋮3n+2\)
3n+2 là ước của 7 \(\Rightarrow3n+2\in\left\{1;7;-1;-7\right\}\)
\(\Rightarrow n\in\left\{-\dfrac{1}{3};\dfrac{5}{3};-1;-3\right\}\)
n thuộc Z \(\Rightarrow n\in\left\{-1;-3\right\}\)
Ta có: \(2n-1⋮3n+2\)
\(\Leftrightarrow3\cdot\left(2n-1\right)⋮3n+2\)
\(\Leftrightarrow6n-3⋮3n+2\)
\(\Leftrightarrow6n+4-7⋮3n+2\)
mà \(6n+4⋮3n+2\)
nên \(-7⋮3n+2\)
\(\Leftrightarrow3n+2\inƯ\left(-7\right)\)
\(\Leftrightarrow3n+2\in\left\{1;-1;7;-7\right\}\)
\(\Leftrightarrow3n\in\left\{-1;-3;5;-9\right\}\)
\(\Leftrightarrow n\in\left\{-\dfrac{1}{3};-1;\dfrac{5}{3};-3\right\}\)
mà \(n\in Z\)
nên \(n\in\left\{-1;-3\right\}\)
Vậy: \(n\in\left\{-1;-3\right\}\)