Question

[Hatsune Miku]

Tìm n thuộc Z để A= n-8/n+1 + n+3/n+1 là 1 số nguyên

Answer 1

[Nguyễn Tất Đạt]

\(A=\frac{n-8}{n+1}+\frac{n+3}{n+1}=\frac{n-8+n+3}{n+1}=\frac{2n-5}{n+1}\)

Để \(A\)là số nguyên thì \(2n-5⋮n+1\)

\(n+1⋮n+1\Rightarrow2\left(n+1\right)⋮n+1\Rightarrow2n+2⋮n+1\)

\(\Rightarrow2n-5-\left(2n+2\right)⋮n+1\Rightarrow2n-5-2n-2⋮n+1\)\(\Rightarrow-7⋮n+1\)

\(\Rightarrow n+1\inƯ\left(7\right)=\left\{1;7;-1;-7\right\}\Rightarrow n\in\left\{0;6;-2;-8\right\}\)

Answer 2

[Hatsune Miku]

thanks bn nhju nha Kurokawa Neko