\(\left(2n+3\right)⋮n\Rightarrow3⋮n\Rightarrow n\inƯ\left(3\right)=\left\{1;-1;3;-3\right\}\)
Do \(n\in N\)
\(\Rightarrow n\in\left\{1;3\right\}\)
Ta có \(\left(2n+3\right)⋮n\) mà \(2n⋮n\) \(\Rightarrow3⋮n\) \(\Rightarrow n\inƯ\left(3\right)\)
\(\Rightarrow n\in\left\{1;-1;3;-3\right\}\)
mà \(n\in N\Rightarrow n\in\left\{1;3\right\}\)
Ta có: \(2n+3⋮n\)
\(\Leftrightarrow3⋮n\)
hay \(n\in\left\{1;-1;3;-3\right\}\)