I guess the key thing to take away from this is that if you're raising, your pot odds aren't a number you can calculate with 100% certainty. Because you're not closing out the action, your pot odds depend on how your opponent reacts to your raise.
Pot is 1000. You and villain both have 5000 left. The villain bets 1000 and you raise to 3000.
If your opponent folds, there are no pot odds for you as the action has ended. If your opponent calls, that makes your pot odds for the raise 4:3 retroactively. If your opponent raises all-in (5000), that makes your pot odds for the raise 6:5 retroactively.
What does this mean with regards to the decision to raise? Since 6:5 is the worst pot odds you could be getting, then it is always profitable to make that raise if you are at least 5/11 or 45.45% to win. Also, if you think your opponent is just calling 75% of the time and raising 25% of the time, your raise is always profitable if you are at least 3/7 * (0.75) + 5/11 * (0.25) = 43.51% to win.
There are a million caveats to this. Firstly, this only tells
you if raising to 3000 is profitable. It doesn't tell you if it's more profitable than calling or raising a different amount. Secondly, these pot odds calculations only apply as above if there's only one more street. If the decision is on the flop, it gets more complicated, because you may be faced with another bet if you miss on the turn. Finally, the most important caveat is that the extra value added by the chance that your opponent folds to your raise is almost always the deciding factor, not these minute differences in projected pot odds. As you can see in the example, the differences are usually minute, and that's only half of the value formula in the first place. It could make a difference in extreme situations, such as a deepstacked scenario where your opponent is super LAG. But I don't think you really need a formula to tell you that you should just call there.
That's a lot of posting to describe a principle that's basically useless in practice.