[tex]\displaystyle\\
\frac{x+2}{x-3}=\frac{x-3+3+2}{x-3}=\frac{x-3+5}{x-3}=\\\\
=\frac{x-3}{x-3}+\frac{5}{x-3}=\boxed{1+\frac{5}{x-3}}\\\\
1\in\mathbb{Z}\\
5~\vdots~(x-3)\\\\
D_5=\{-5;~-1;~1;~5\} \\\\
x-3=-5~\Longrightarrow~x=-5+3~\Longrightarrow~x=\boxed{-2}\\
x-3=-1~\Longrightarrow~x=-1+3~\Longrightarrow~x=\boxed{2}\\
x-3=1~\Longrightarrow~x=1+3~\Longrightarrow~x=\boxed{4}\\
x-3=5~\Longrightarrow~x=5+3~\Longrightarrow~x=\boxed{8}\\\\
\boxed{\bf A=\{-2;~2;~4;~8\} }\\
\boxed{\bf\text{\bf Card}~A=4}[/tex]
