\(A=\dfrac{3x-1}{x+2}\inℕ\left(x\inℕ;x\ne-2\right)\)
\(\Rightarrow3x-1⋮x+2\)
\(\Rightarrow3x-1-3\left(x+2\right)⋮x+2\)
\(\Rightarrow3x-1-3x-6⋮x+2\)
\(\Rightarrow-7⋮x+2\)
\(\Rightarrow x+2\in U\left(7\right)=\left\{1;7\right\}\)
\(\Rightarrow x\in\left\{-1;5\right\}\)
\(\Rightarrow x\in\left\{5\right\}\left(x\inℕ\right)\)