I have a ratio:

A/B the value of which is known e.g. 0.34 but I don't know A or B.

Apparently, if you divide A/B by (1 + A/B), you get A/(A+B).

I can do that maths to prove that this is the case, I don't understand the logic behind doing thing however.

In other words, how do I know to even attempt to convert A/B into A/(A+B)?