\(\Rightarrow2x+1⋮x-3\\ \Rightarrow2x+1⋮2\left(x-3\right)\\ \Rightarrow2x+1⋮2x-6\\ \Rightarrow\left(2x+1\right)-\left(2x-6\right)⋮x-3\\ \Rightarrow7⋮x-3\\ \Rightarrow x-3\inƯ\left(7\right)=\left\{\pm7;\pm1\right\}\)
\(\Rightarrow x=\left\{10;-4;4;2\right\}\)