a, Vì : \(n+2⋮n-1\) mà \(n-1⋮n-1\)
\(\Rightarrow\left(n+2\right)-\left(n-1\right)⋮n-1\)
\(\Rightarrow n+2-n+1⋮n-1\Rightarrow3⋮n-1\)
\(\Rightarrow n-1\in\left\{\pm1;\pm3\right\}\)
+) Nếu : n - 1 = 1 => n = 1 + 1 => n = 2
+) Nếu : n - 1 = -1 => n = -1 + 1 => n = 0
+) Nếu : n - 1 = 3 => n = 3 + 1 => n = 4
+) Nếu : n - 1 = -3 => n = -3 + 1 => n = -2
Vậy \(n\in\left\{2;0;4;-2\right\}\)
b, Vì : \(3n-5⋮n-2\) (1)
Mà : \(n-2⋮n-2\Rightarrow3\left(n-2\right)⋮n-2\Rightarrow3n-6⋮n-2\) (2)
Từ (1) và (2) \(\Rightarrow\left(3n-5\right)-\left(3n-6\right)⋮n-2\)
\(\Rightarrow3n-5-3n+6⋮n-2\Rightarrow1⋮n-2\)
\(\Rightarrow n-2\in\left\{1;-1\right\}\Rightarrow n\in\left\{1;3\right\}\)
Vậy \(n\in\left\{1;3\right\}\)
