\(2n+5⋮n+1\)
\(2n+2+3⋮n+1\)
\(2\left(n+1\right)+3⋮n+1\)
Vì \(2\left(n+1\right)⋮n+1\)
\(\Rightarrow3⋮n+1\)
\(\Rightarrow n+1\inƯ\left(3\right)=\left\{1;3;-1;-3\right\}\)
\(\Rightarrow n\in\left\{0;2;-2;-4\right\}\)
Mà \(n\inℕ^∗\Rightarrow n\in\left\{0;2\right\}\)
Vậy.......