(1 + x)/(1 - x) - (1 - x)/(1 + x)/((1 + x)/(1 - x)) - (1 - 1/(1 + x))=
=(1 + x)/(1 - x) - (x - 1)^2/(x + 1)^2 - x/(x + 1)=
=((1 + x)·(x + 1)^2 - (x - 1)^2·(1 - x) - x·(x + 1)·(1 - x))/((x + 1)^2·(1 - x))=
=((x + 1)^3 - (1 - x)^3 - (x - x^3))/((x + 1)^2·(1 - x))=
=((x^3 + 3·x^2 + 3·x + 1) - (- x^3 + 3·x^2 - 3·x + 1)+
- (x - x^3))/((x + 1)^2·(1 - x))=
=(3·x^3 + 5·x)/((x + 1)^2·(1 - x))