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I thought up what shouldd be an extremely simple problem but am having trouble with the math, I'm sure one of you guys can probably help me out with it.

Events A and B occur with a time separation in the laboratory frame but no space separation, I thought it'd be easy to prove that in a rocket frame moving with a [tex]\beta[/tex] speed to the right relative to the laboratory frame the space separation divided by the time separation of the events would be [tex]-\beta[/tex] (that is [tex]dx'/dt'=-\beta[/tex])

[tex]dt^2-dx^2 = dt'^2-dx'^2[/tex]

Since the events occur in the same place in the laboratory frame

[tex]dt^2 = dt'^2-dx'^2[/tex]

After Lorentz transformation

[tex] ( \frac{dt' + dx'\beta} { \sqrt{1-\beta^2}} )^2 = dt'^2-dx'^2 [/tex]

However, I've been unable to derive this properly, is it just lack of math skills or did I set the equations inproperly? Any help is appreciated.