Suppose in the rest frame $S$, event $A$ occurs at $x = 0, t =0$ and event $B$ occurs at $x = 100, t = 80$.
Now suppose that frame $S’$ is moving with velocity $V$ with respect to $V$.
Now the question is what is the distance between the events in frame $S’$. Since the events occur at different times in the rest frame I was wondering if it is applicable to use the formula $L = L_0/\gamma$.
On the other hand if i transform the $x$ cords for both events using Lorentz transforms and subtract them i get $x_B’ - x_A’ = \gamma ( x_B - \beta ct_B - x_1 + \beta ct_A)$. In this instance since $t_B \neq t_A$ you will get a different answer than if you use Lorentz contradiction formula.
So since both approaches yield different answers, I was wondering which one is correct and what the fallacy with the other one is.