Bài 3:Để A là số nguyên thì \(2n+7⋮n+3\)=>\(2n+6+1⋮n+3\)=>\(1⋮n+3\)=>\(n+3\in\left\{1;-1\right\}\)=>\(n\in\left\{-2;-4\right\}\)Bài 4:Để A là số nguyên thì \(2n+7⋮n+1\)=>\(2n+2+5⋮n+1\)=>\(5⋮n+1\)=>\(n+1\in\left\{1;-1;5;-5\right\}\)=>\(n\in\left\{0;-2;4;-6\right\}\)Bài 5:Để A là số nguyên thì \(6n-3⋮3n+1\)=>\(6n+2-5⋮3n+1\)=>\(-5⋮3n+1\)=>\(3n+1\in\left\{1;-1;5;-5\right\}\)=>\(3n\in\left\{0;-2;4;-6\right\}\)=>\(n\in\left\{0;-\dfrac{2}{3};\dfrac{4}{3};-2\right\}\)mà n nguyên nên \(n\in\left\{0;-2\right\}\)Bài 6:Để A là số nguyên thì \(3n+4⋮n-1\)=>\(3n-3+7⋮n-1\)=>\(7⋮n-1\)=>\(n-1\in\left\{1;-1;7;-7\right\}\)=>\(n\in\left\{2;0;8;-6\right\}\)Câu trả lời: Bài 3:Để A là số nguyên thì \(2n+7⋮n+3\)=>\(2n+6+1⋮n+3\)=>\(1⋮n+3\)=>\(n+3\in\left\{1;-1\right\}\)=>\(n\in\left\{-2;-4\right\}\)Bài 4:Để A là số nguyên thì \(2n+7⋮n+1\)=>\(2n+2+5⋮n+1\)=>\(5⋮n+1\)=>\(n+1\in\left\{1;-1;5;-5\right\}\)=>\(n\in\left\{0;-2;4;-6\right\}\)Bài 5:Để A là số nguyên thì \(6n-3⋮3n+1\)=>\(6n+2-5⋮3n+1\)=>\(-5⋮3n+1\)=>\(3n+1\in\left\{1;-1;5;-5\right\}\)=>\(3n\in\left\{0;-2;4;-6\right\}\)=>\(n\in\left\{0;-\dfrac{2}{3};\dfrac{4}{3};-2\right\}\)mà n nguyên nên \(n\in\left\{0;-2\right\}\)Bài 6:Để A là số nguyên thì \(3n+4⋮n-1\)=>\(3n-3+7⋮n-1\)=>\(7⋮n-1\)=>\(n-1\in\left\{1;-1;7;-7\right\}\)=>\(n\in\left\{2;0;8;-6\right\}\)