Let us just start with the following line of work, which starts off by assuming that the Lorentz transformations are correct:
Equation 1: v = \frac{x^\prime}{t^\prime} = \frac{x-vt}{t-vx/c^2}
Lorentz Transformations
x^\prime = { { x - vt } \over \sqrt { 1 - { v^2 \over c^2 } } }...
Lorentz coordinate transformations
x^\prime = { { x - vt } \over \sqrt { 1 - { v^2 \over c^2 } } }
t^\prime = { { t - { v \over c^2 } x } \over \sqrt { 1 - { v^2 \over c^2 } } }
We can undo the division by zero error that occurs in the Lorentz transformations when v=c, if we...
A derivation of the Lorentz transformations can be found here Darkstar:
http://casa.colorado.edu/~ajsh/sr/construction.html
It seems that you presumed that the distance traveled by the unprimed frame is "Lorentz contracted," rather than using the Lorentz coordinate transformation? Why did...