[tex]\it x\in\mathbb{N,}\ \ 2x+3\ \vdots\ x+1 \Rightarrow x+1 | 2x+3 \ \ \ \ \ (1)\\ \\ x+1|x+1\Rightarrow x+1|(x+1)\cdot2 \Rightarrow x+1|2x+2\ \ \ \ \ (2)\\ \\ (1),\ (2) \Rightarrow x+1|2x+3-2x-2 \Rightarrow x+1|1 \Rightarrow x+1=1 \Rightarrow x=0[/tex]
