Equalities in Groups, How prove this? Let $ H,K≤ G$,  for all $g ∈  G $ ,
$$ \frac {|H||K|}{|H∩(gKg^{-1})|}= \frac {|H||K|}{|(g^{-1}Hg)∩ K|} $$
I try to show this but I do Know how to attack this exercise.

It follows from $|H\cap (gKg^{-1})|=|g^{-1}(H\cap (gKg^{-1}))g|=|g^{-1}Hg\cap K|$.
