Math Help - simplify this function

1. simplify this function

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.

2. (1+s^2)^-1 = (1+s^2)^0 - (1+s^2)^-1 = 1/ 1+s^2
times s^2
= s^2/ 1+ s^2

:O
correct me if I'm wrong

3. Ni hao! and thanks for the help.

(1+s^2)^-1 = 1/ 1+s^2
times s^2
= s^2/ 1+ s^2

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(1+s^2)^-1 = 1/ 1+s^2 - yes understand that
times s^2 - why?

how did you know to multiply by s^2 at the end?
What were the algebraic steps on the run up to that answer?

feichang ganxing =]