Answer
$\frac{x^2-1}{x^2+1}$; see graph.
Work Step by Step
Step 1. Multiply the numerator and the denominator with $x$. We have
$f(x)=\frac{x^2-1}{x^2+1}$
where $x\ne 0$ with a hole at $(0,-1)$
Step 2. There are no vertical asymptotes.
Step 3. We can identify a horizontal asymptote as $y=1$
Step 4. We can find the x-intercepts at $(\pm1,0)$
Step 5. As $f(-x)=f(x)$, the function is symmetric with respect to the y-axis.
Step 6. Based on the above results, we can graph the function as shown in the figure.
