ĐKXĐ: n<>-1
Để A là số nguyên thì \(12n⋮3n+3\)
=>\(12n+12-12⋮3n+3\)
=>\(3n+3\inƯ\left(-12\right)\)
=>\(3n+3\in\left\{1;-1;2;-2;3;-3;4;-4;6;-6;12;-12\right\}\)
=>\(n\in\left\{-\dfrac{2}{3};-\dfrac{4}{3};-\dfrac{1}{3};-\dfrac{5}{3};0;-2;\dfrac{1}{3};-\dfrac{7}{3};1;-3;3;-5\right\}\)