ta có:\(\frac{n-7}{n+1}=\frac{n+1-8}{n+1}=1-\frac{8}{n+1}\)
để \(n-7⋮n+1\Rightarrow\frac{n-7}{n+1}\in Z\)
\(\Rightarrow1-\frac{8}{n+1}\in Z\Leftrightarrow\frac{8}{n+1}\in Z\)
\(\Rightarrow n+1\inƯ\left(8\right)=\left\{\pm1;\pm2;\pm4;\pm8\right\}\)
do n nguyên dương nên \(\Rightarrow n+1\in\left\{1;2;4;8\right\}\)
bạn tính nốt n nhé