\(2x+1⋮x-5\)
mà \(2\left(x-5\right)⋮x-5\)
\(\Rightarrow2x+1-2\left(x-5\right)⋮x-5\)
\(\Rightarrow2x+1-2x+10⋮x-5\)
\(\Rightarrow9⋮x-5\)
\(\Rightarrow x-5\inƯ\left(9\right)=\left\{1;-1;3;-3;9;-9\right\}\)
Ta có bảng sau:
x-5 | 1 | -1 | 3 | -3 | 9 | -9 |
x | 6 | 4 | 8 | 2 | 14 | -4 |
Vậy \(x\in\left\{-4;2;4;6;8;14\right\}\)