H, K sub-groups of a group G. x,y elements of G. Suppose Hx=Ky. Show that x(y^-1) is an element of H, and deduce that H = K.

I just multiplied x^-1 to get H=Ky(x^-1), to get yx^-1 element of H, since H is a sub-group, it's inverse, y^-1x is also an element of H...

can i say that?

How would I show that H = K?

Thanks!