\(A=\dfrac{n+7}{n+5};A\in Z\)
\(\Leftrightarrow n+7⋮n+5\)
\(n+5+2⋮n+5\Rightarrow2⋮n+5\)
\(\Rightarrow n+5\inƯ\left(2\right)\)
\(Ư\left(2\right)=\left\{\pm1;\pm2\right\}\)
\(\Leftrightarrow n+5=1\Rightarrow n=-4\)
\(\Leftrightarrow n+5=-1\Rightarrow n=-6\)
\(\Leftrightarrow n+5=2\Rightarrow n=-3\)
\(\Leftrightarrow n+5=-2\Rightarrow n=-7\)
A =\(\dfrac{n+7}{n+5}\) là số nguyên
=> (n +7 ) \(⋮\)( n+5)
=> ( n + 5 + 2)\(⋮\) ( n+ 5)
=> 2 \(⋮\) ( n + 5)
=> n + 5 \(\in\) Ư( 2)
=> n + 5 \(\in\) { -2 ; -1 ; 1; 2 }
Vì n \(\in\) Z
=> n \(\in\) { -7;-6 ; -4 ; -3 }
Vậy :=> n \(\in\) { -7;-6 ; -4 ; -3 }
