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# Thread: Should be easy, but I'm not getting it somehow

1. ## Should be easy, but I'm not getting it somehow

Hello ... I've got a Jacobian transformation problem that starts with two variables, X1 and X2, each of which need to be put into terms of Y1 and Y2.

I start with Y1 = X1 + X2 and Y2 = X1/X2.

Of course, I should end up with expressions for X1 and X2 in terms of Y1 and Y2, but I keep coming up with things that reduce to X1=X1, or something equally useless.

I recognize that in Jacobian transformations, this should actually be one of the easier phases of the problem; it needs to be finished early and without undue delay. I have a feeling that this solution should be terribly obvious, maybe I've just outsmarted myself with this one.

Is the solution as easy to get as it appears? I must be missing something fairly obvious. I've been provided with final answers, but no idea of how they were arrived at. Any help at all is greatly appreciated.

2. If it's any help, I have the final answers:

X1 = Y1(Y2)/(1+Y2) and X2 = (Y1)/(1+Y2)

The problem is, I don't see how to derive them. I suppose I could just start from X1 = X1 (for example), and then just start replacing one of the X1's with Y1's and Y2's; but each replacement seems to require adding both an X1 and an X2, so that's very tricky. I guess I have to find a way where one X1 is replaced by a complex fraction with X2 in both the numerator and denominator (ultimately allowing X2's to be cancelled out), but that still eludes me.

3. Y1 = X1 + X2 and Y2 = X1/X2.

Then 2nd equation implied that X1 = Y2X2.

Plug that into first equation to get

Y1 = Y2X2 + X2 = X2(Y2+1) i.e. X2 = Y1/(Y2+1)

You know that X1 = Y2X2 = Y2Y1/(Y2+1)

4. Thank You!

That was thorny, since a Jacobian problem has so much more work to be done after that part's complete.