Originally Posted by
woolyhead Thanks Ackbeet and Waqarhaider. I tried your suggestions and they worked, but I still cannot visualise or imagine why we let the numerator and the denominator of the original expression equal zero, even though I know the method given uses this trick. Should I just use the method and stop asking questions about the reasons why it works, then? Wouldn't that reduce the intellectual content of the approach somewhat? Suppose I came across another type of problem where a full understanding the method used in the present problem could be of help. Just knowing a method that works without knowing why it works wouldn'd be a lot of use, would it? Can you also please help me understand what's going on with the method you kindly gave me.
As I see it, the original equation describes two 2D surfaces which can be moved up or down according to the value of the constants. These constants are in the way, so to speak, of our calling the expression homogenous, so we use your trick to get rid of them in order to be able to use the standard method for solving such equations. So what are we achieving by making the numerator and the denominator zero? Where's the logic in it?