The range of  $\frac{x^2+2x+1}{x^2+2x-1}$  is

Let $y=\frac{x^2+2x+1}{x^2+2x-1}\Rightarrow (y-1)x^2+(2y-2)x-(y+1)=0$

  $\Rightarrow {(2y-2)}^2+4(y-1)(y+1)\ge 0$$\begin{array}{l}\Rightarrow 4y^2-8y+4+4(y^2-1)\ge 0\Rightarrow 8y^2-8y\ge 0\\ \Rightarrow y\le 0ory\ge 1buty\ne 1\end{array}$

Range of y is  $(-\infty ,0]\cup (1,\infty )$