I am slightly confused about the Lorentz transformation for time
$t=\gamma (t'+\frac {vx'}{c^2}) $
I have seen the derivation and understand it (maybe there are several and some are able to explain my question better than others? The derivation I have seen is considering how the x components transform using a simple geometric/algebraic approach of reference frames coinciding, and then using the results for the x transformation to obtain the time transformations)
What I do not understand is why the time is not simply
$t'=t/{\gamma} $
which is the simple result obtained at the beginning of any special relativity book for the time intervals on a moving and stationary clock evaluated by an observer. In essence, why do we have the Lorentz transformations if we have the previous easy result, and how are the Lorentz transformations consistent with the previous results? They clearly are not algebraically equivalent...