\(A=\dfrac{6n+42}{6n}\)
\(\Rightarrow6n+42⋮6n\)
\(\Rightarrow42⋮6n\)
\(\Rightarrow6n\inƯ\left(42\right)\)
\(\Rightarrow6n\inƯ\left(42\right)=\left\{1;2;3;6;7;14;21;42;-1;-2-3;-6;-7;-14;-21;-42\right\}\)
\(\Rightarrow6n\in\left\{\dfrac{1}{6};\dfrac{1}{3};\dfrac{1}{2};1;\dfrac{7}{6};\dfrac{7}{3};\dfrac{7}{2};7;-\dfrac{1}{6};-\dfrac{1}{3};-\dfrac{1}{2};-1;-\dfrac{7}{6};-\dfrac{7}{3};-\dfrac{7}{2};-7\right\}\)
Mà \(n\in Z;n\ne0\)
\(\Rightarrow n\in\left\{1;7\right\}\)
