calculus - $dx=frac {dx}{dt}dt$. Why is this equality true and what does it mean?

$dx=\frac {dx}{dt}dt$. I know that this deduction is obvious from the chain rule, given that we treat our dx and dt as just numbers. But I find it quite unsatisfactory to think of it in that sense. Is there a better / more "calculus-inclined" way of thinking about this equality. Can you please explain both the LHS and RHS individually.