\(A=\frac{2x+3}{2x-3}\)
\(A=\frac{2x-3+6}{2x-3}=1+\frac{6}{2x-3}\)
để \(A\in Z\Rightarrow\frac{6}{2x-3}\in Z\Rightarrow6⋮2x-3\)
\(\Rightarrow2x-3\inƯ\left(6\right)=\left\{\pm1,\pm2,\pm3,\pm6\right\}\)
vì 2x-3 là số lẻ
\(\Rightarrow2x-3=\left\{\pm1,\pm3\right\}\Rightarrow x=\left\{2,1,3,0\right\}\)