\(\frac{x+11}{x+2}\in N\)
\(\Rightarrow\left(x+11\right)⋮\left(x+2\right)\)
\(\Rightarrow\left(x+2+9\right)⋮\left(x+2\right)\)
Vì \(x+2⋮x+2\Rightarrow9⋮\left(x+2\right)\)
\(\Rightarrow\left(x+2\right)\in\left(1;3;9\right)\)
Vì x thuộc N \(\Rightarrow n\in\left(1;7\right)\)
\(\frac{11+x}{2+x}=\frac{9+2+x}{2+x}=\frac{9}{2+x}+\frac{2+x}{2+x}.\)
\(\Rightarrow\)Để \(11+x⋮2+x\)thì 9 phải chia hết cho x + 2 hay x + 2 là Ư(9)
\(\Rightarrow x+2\in\left\{1;3;9\right\}\)
\(\Rightarrow x=\left\{1;7\right\}\)
\(\frac{x+11}{x+2}\) ∈ \(ℕ\)
⇒(x+11)⋮(x+2)
⇒(x+2+9)⋮(x+2)
Vì x+2⋮x+2⇒9⋮(x+2)
⇒(x+2)∈(1;3;9)
Vì x thuộc N ⇒n∈(1;7)