ĐK: \(x\ne\pm1\)
\(\dfrac{x^2+mx+2}{x^2-1}=1\)
\(\Leftrightarrow x^2+mx+2=x^2-1\)
\(\Leftrightarrow mx=-3\)
Yêu cầu bài toán thỏa mãn khi \(\left[{}\begin{matrix}m=0\\-\dfrac{3}{m}=\pm1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}m=0\\m=\pm3\end{matrix}\right.\)
Vậy \(m=0;m=\pm3\Rightarrow A\)