Well, take a look at what happens when you fill in your intermediate terms instead of using their results:
(16 - 9) * 1 / (1 - (9 / 16)) = 15,9999 ~ 16
16 * (9 / 16) = 9
So at least the second part will always work, but it’s also completely pointless since you need to know the ratio in advance for it to give the correct result
You really shouldn’t just randomly throw together expressions not knowing what you’re doing...