\(3n+9⋮2n-1\)
\(\Leftrightarrow6n+18⋮2n-1\)
\(\Leftrightarrow2n-1\in\left\{1;-1;3;-3;7;-7;21;-21\right\}\)
\(\Leftrightarrow2n\in\left\{2;0;4;-2;8;-6;22;-20\right\}\)
hay \(n\in\left\{1;0;2;-1;4;-3;11;-10\right\}\)
\(\left(3n+9\right)⋮\left(2n-1\right)\)
\(\Rightarrow\left\{{}\begin{matrix}\left(3n+9\right)⋮\left(2n-1\right)\\\left(2n-1\right)⋮\left(2n-1\right)\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}\left(6n+18\right)⋮\left(2n-1\right)\\\left(6n-3\right)⋮\left(2n-1\right)\end{matrix}\right.\)
\(\Rightarrow\left(6n+18\right)-\left(6n-3\right)⋮\left(2n-1\right)\)
\(\Rightarrow21⋮\left(2n-1\right)\)
\(\Rightarrow\left(2n-1\right)\inƯ\left(21\right)=\left\{-21;-7;-3;-1;1;3;7;21\right\}\)
\(\Rightarrow n\in\left\{-10;-3;-1;0;1;2;4;11\right\}\)
