r(s)= ((1+s^2)^-1, root 2 s(1+s^2)^-1, 1- (1+s^2)^-1

I understand this simplification up to a point:

r(s)= 1+s^2)^-1 (1, root2 s, s^2) (green i understand, red i dont)

the (1+s^2)^-1 substitutes nicely for the first 2 sections, but what is the algebra required for the last part?

I mean s^2 multiplied by (1+s^2)^-1 is equal to 1- (1+s^2)^-1 but I cannot work out how to derive this.

Can anyone help please?