If f(x)=x2−1x2+1, for every real number, then minimum value of f

We have f(x)=1−2x2+1f(x) will be minimum if 2/x2+1 is maximum i.e. if x2+1 is least i.e. when x=0. Thus minimum value of f(x)  is  f (0)  =   −1