Find the extremum of function y = (2x / x ^ 2 + 1) - 2

Find the extremum of function y = (2x / x ^ 2 + 1) - 2

When x ≥ 0
y=(2x/x^2+1)-2
=2/(x+1/x)-2
≤2/2-2
=-1
When x ≤ 0
y=(2x/x^2+1)-2
=2/(x+1/x)-2
≥-2/2-2
=-3
So the range is [- 3, - 1]