\(a,n+9⋮n+2.\)
\(\Rightarrow\left(n+2\right)+7⋮n+2.\)
mà \(n+2⋮n+2\Rightarrow7⋮n+2\Rightarrow n+2\in U_{\left(7\right)}=\left\{1;7\right\}.\)
\(\Rightarrow n\in\left\{-1;-9\right\}.\)
Vậy--..
\(b,2n+9⋮n-1.\)
\(\Rightarrow\left(2n-2\right)+11⋮n-1.\)
\(\Rightarrow2\left(n-1\right)+11⋮n-1.\)
mà \(2\left(n-1\right)⋮n-1\Rightarrow11⋮n-1\Rightarrow n-1\in U_{\left(11\right)}=\left\{1;11\right\}.\)
\(\Rightarrow n\in\left\{2;12\right\}.\)
Vậy--..
\(c,3n+5⋮2n+1.\)
\(\Rightarrow2\left(3n+5\right)⋮2n+1.\)
\(\Rightarrow6n+10⋮2n+1.\)
\(\Rightarrow\left(6n+3\right)+7⋮2n+1.\)
\(\Rightarrow3\left(2n+1\right)+7⋮2n+1.\)
mà \(3\left(2n+1\right)⋮2n+1\Rightarrow7⋮2n+1\Rightarrow2n+1\in U_{\left(7\right)}=\left\{1;7\right\}.\)
\(\Rightarrow n\in\left\{0;3\right\}.\)
Vậy--..
