\(x+16⋮x+1\)
\(\Rightarrow x+1+15⋮x+1\)
\(x+1⋮x+1\Rightarrow15⋮x+1\)
\(\Rightarrow x+1\inƯ\left(15\right)\)
\(Ư\left(15\right)=\left\{\pm1;\pm3;\pm5;\pm15\right\}\)
\(\Rightarrow\left[{}\begin{matrix}x+1=1\Rightarrow x=0\\x+1=-1\Rightarrow x=-2\\x+1=3\Rightarrow x=2\\x+1=-3\Rightarrow x=-4\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x+1=5\Rightarrow x=4\\x+1=-5\Rightarrow x=-6\\x+1=15\Rightarrow x=14\\x+1=-15\Rightarrow x=-16\end{matrix}\right.\)
