Ok, what's going on here is that in the process of solving an equation, sometimes you introduce spurious roots. Here's a very simple example: solve subject to So the first thing you'd do, obviously, is take the square root of both sides. That gives you But the problem statement said that had to be positive. Evidently, the negative solution is spurious. Therefore, the solution to the problem is exactly
In your case, you'd solve the problem by multiplying through by . The problem is, is not in the solution space of the original problem, because you'd divide by zero. However, multiplying through by the factor masks that fact.
You ALWAYS have to go back and double-check your answers, to see if they fit the original problem, and if they make sense. And that is for this very reason.
Does that make sense?