$$\sigma(z) = \frac{e^x}{e^x + 1}$$
$$\sigma(z) = \frac{1}{e^{-x} + 1}$$
They are both the same but I'm unable to rewrite one to the other. I'm learning about neural networks for fun and I understand what it does. I find the first equation more intuitive to understand than the second equation, which is why I'd want to be able to understand how to rewrite it.
I have a couple of questions:
How would I Google for this question? I think even in Dutch (my native language) I'd have trouble in this.
How do you rewrite one equation to the other? I've seen a couple of blogs doing it, but I didn't save it. It involved some +1 and -1 trickery.
I don't know how to search for it. And it may be the case that this answer has already been answered on Stack Exchange, but I couldn't find it via Google. The search term scavenger hunt has taken 1 hour already.