\(A=\dfrac{n+3}{n-2}=\dfrac{n-2+5}{n-2}=\dfrac{n-2}{n-2}+\dfrac{5}{n-2}=1+\dfrac{5}{n-2}\)
\(\Rightarrow5⋮n-2\)
\(\Rightarrow n-2\inƯ\left(5\right)\)
\(Ư\left(5\right)=\left\{\pm1;\pm5\right\}\)
\(\Rightarrow\left[{}\begin{matrix}n-2=1\Rightarrow n=3\\n-2=-1\Rightarrow n=1\\n-2=5\Rightarrow n=7\\n-2=-5\Rightarrow n=-3\end{matrix}\right.\)