Ta có: \(2x-5⋮x+1\)
\(\Leftrightarrow2x+2-7⋮x+1\)
Mà: \(2x+2⋮x+1\)
\(\Leftrightarrow7⋮x+1\)
\(\Leftrightarrow x+1\inƯ_{\left(7\right)}=\left\{-7;-1;1;7\right\}\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=-7\\x+1=-1\\x+1=1\\x+1=7\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-8\\x=-2\\x=0\\x=6\end{matrix}\right.\)
Vậy: \(x=-8;-6;0;6\)
_Chúc bạn học tốt_