$(3n-1)\vdots(n+2)$
$\Rightarrow 3(n+2)-7\vdots(n+2)$
$\Rightarrow (n+2)\in{Ư(7)=\text{{±1; ±7}}}$
$\Rightarrow n\in{\text{{-1; -3; 5; -9}}}$
$(2n+1)\vdots(n+3)$
$\Rightarrow 2(n+3)-5\vdots(n+3)$
$\Rightarrow (n+3)\in{Ư(5)=\text{{±1; ±5}}}$
$\Rightarrow n\in{\text{{-2; -4; 2; -8}}}$