[tex]x^2+2x+1=x^2+x+x+1=x(x+1)+1(x+1)=(x+1)(x+1)\\----------------------\\2x+2=2(x+1)\\----------------------\\\\\dfrac{2x+2}{x^2+2x+1}=\dfrac{2(x+1)}{(x+1)(x+1)}\\\\\text{Canceled}\ (x+1)\\\\=\boxed{\dfrac{2}{x+1}}[/tex]
