Question

How is 1+(x^2)/(1-(x^2)) = -1 +2/(1-x^2)? Please leave a detailed explanation

Answer 1

Consider the following expression in terms of `x`:

`E(x) = (1+x^2)/(1-x^2)=-(-1-x^2)/(1-x^2)`

We see that adding `2` to the numerator makes it the same as the denominator. In order to keep it equivalent, we have to substract `2` afterwards:

`E(x) = -(color(red)2-1-x^2-color(red)2)/(1-x^2)=-(1-x^2-2)/(1-x^2)`

`E(x) = -[(1-x^2)/(1-x^2)-2/(1-x^2)]`

`E(x)=-[1-2/(1-x^2)]= -1+2/(1-x^2)`