Răspuns:
(n+1)/(n+1)+9/(n+1)=1+9/(n+1) n+1=D 9 ; n+1=1 ; n=0 ; n+1=3 ; n=2 ; n+1=9 ; n=8
Explicație pas cu pas:
[tex]\it n\in\mathbb{N,\ \ } \dfrac{n+10}{n+1}\in\mathbb{N} \Rightarrow n+1|n+10\ \ \ \ \ (1)\\ \\ \\ Dar,\ \ n+1|n+1\ \ \ \ \ \ (2)\\ \\ \\ (1),\ (2)\Rightarrow n+1|n+10-n-1\Rightarrow n+1|9\Rightarrow n+1\in\{1,\ 3,\ 9\}|_{-1}\Rightarrow \\ \\ \\ \Rightarrow n\in\{0,\ \ 2,\ \ 8\}[/tex]