Ta có: $n+9$ ⋮ $n+6$
$⇒(n+6)+3$ ⋮ $n+6$
$⇒3$ ⋮ $n+6$
$⇒n+6∈Ư(3)=\{±1;±3\}$
Ta có bảng sau:
n+6 -1 1 -3 3
n -7 -5 -9 -3
Vậy $n∈\{-6;-5;-9;-3\}$
Ta có: $n+8$ ⋮ $n+2$
$⇒(n+2)+6$ ⋮ $n+2$
$⇒6$ ⋮ $n+2$
$⇒n+2∈Ư(6)=\{±1;±2;±3;±6\}$
Ta có bảng sau:
n+2 -1 1 -2 2 -3 3 -6 6
n -3 -1 -4 0 -5 1 -8 4
Vậy $n∈\{-3;-1;-4;0;-5;1;-8;4\}$.