#### Answer

The equation of the compressed graph is $$y=\frac{x^2+1}{2x^2}$$

#### Work Step by Step

For $c\gt1$, the graph is scaled:
- $y=cf(x)$ - stretched - vertically - factor of $c$
- $y =\frac{1}{c}f(x)$ - compressed - vertically - factor of $c$
- $y=f(cx)$ - compressed - horizontally - factor of $c$
- $y=f(\frac{x}{c})$ - stretched - horizontally - factor of $c$
$$y=1+\frac{1}{x^2}$$
The graph is COMPRESSED - VERTICALLY - by a factor of $2$.
Therefore, the equation of the new graph is $$y = \frac{1}{2}\Big[1+\frac{1}{x^2}\Big]$$
$$y = \frac{1}{2}+\frac{1}{2x^2}$$
$$y=\frac{x^2+1}{2x^2}$$