Ta có: \(5n+14⋮n+2\)
\(\Leftrightarrow5n+10+4⋮n+2\)
mà \(5n+10⋮n+2\)
nên \(4⋮n+2\)
\(\Leftrightarrow n+2\inƯ\left(4\right)\)
\(\Leftrightarrow n+2\in\left\{1;-1;2;-2;4;-4\right\}\)
\(\Leftrightarrow n\in\left\{-1;-3;0;-4;2;-6\right\}\)
mà \(n\in N\)
nên \(n\in\left\{0;2\right\}\)
Vậy: Để \(5n+14⋮n+2\) và \(n\in N\) thì \(n\in\left\{0;2\right\}\)