Để \(A\) là số nguyên thì :
\(2x+3⋮x-1\)
Mà \(x-1⋮x-1\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x+3⋮x-1\\2x-2⋮x-1\end{matrix}\right.\)
\(\Leftrightarrow5⋮x-1\)
\(\Leftrightarrow x-1\inƯ\left(5\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=1\\x-1=5\\x-1=-1\\x-1=-5\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=6\\x=0\\x=-4\end{matrix}\right.\)
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