[tex]2x+\sqrt{(2x)^2+1}=(y+1)+\sqrt{(y+1)^2+1} \Leftrightarrow \frac{1}{\sqrt{(2x)^2+1}-2x}=\frac{1}{\sqrt{(y+1)^2+1}-(y+1)}\Leftrightarrow \sqrt{(2x)^2+1}-2x=\sqrt{(y+1)^2+1}-(y+1)\Rightarrow 2x+\sqrt{(2x)^2+1}-[\sqrt{(2x)^2+1}-2x]=(y+1)+\sqrt{(y+1)^2+1}-[\sqrt{(y+1)^2+1}-(y+1)]\Rightarrow 2x=y+1[/tex]