I do think the formula isn't so simple though. There are people who have difficult lives regardless of their emunah. Let us not forget the Job paradigm. Your formula seems to say, if you are suffering, it is because of your failings in emunah. This is a mistake I believe. The workings of emunah and fate are much more complex than that.
Nevertheless, it still pays to work on emunah and to always try to see Hashem's hand in the world. So your message is useful, but I think it may shame people who have suffered enough.