\(A=\dfrac{x^2-2x+7}{x^2-2x+3}=1+\dfrac{4}{x^2-2x+3}=1+\dfrac{4}{\left(x-1\right)^2+2}\)
\(A\in Z\Leftrightarrow\)\(\left[\left(x-1\right)^2+2\right]\inƯ\left(4\right)=\left\{\pm1;\pm2;\pm4\right\}\)
\(\Rightarrow\left(x-1\right)^2+2=2\)
\(\Leftrightarrow x=0\)