I want to proof that:$\frac{exp(8)}{exp(8)+exp(10)}=\frac{exp(0)}{exp(0)+exp(2)}$
So, my idea is to inverse the fraction and split it. I'd end up with $1+exp(2)$ which is the inverse of the right side of the equation. Is inversing necessary or even allowed to proof the desired?
$\left ( \frac{exp(8)}{exp(8)+exp(10)}\right )^{-1}=\frac{exp(8)+exp(10)}{exp(8)}=\frac{exp(8)}{exp(8)}+\frac{exp(10)}{exp(8)}=1+exp(2)$
This is $$\exp(8)+\exp(10)=\exp(8)+\exp(8)\cdot \exp(2)$$