Why $1/(1+e^{-x}) = e^x/(1+e^x)$ I am currently learning the sigmoid/logistic function and have completely forgotten how the maths behind this equivalence works:
$$
\dfrac{1}{1+ e^{-x}} = \dfrac{e^{x}}{1+e^{x}}
$$
By this I mean how the left side equates with the right side. I know that the left side is simply multiplied by (1/exp(x)) but what are the rules governing this?
Any help would be much appreciated, especially the rules so that I can revisit them.

It is easy.
$ \dfrac{1}{1+ e^{-x}} = \dfrac{e^{x}}{1+e^{x}} $
Consider lhs
$ \dfrac{1}{1+ \frac{1}{e^{x}}} $
which is equal to
$ \dfrac{e^{x}}{e^{x}+ 1} $
