[(x-3)/(2x-4)]/[(x^2-9)/(x-2)]
={(x-3)/[2(x-2)]}/{[(x+3)(x-3)]/(x-2)}
={(x-3)/[2(x-2)]}{(x-2)/[(x+3)(x-3)]}
=[(x-3)(x-2)]/[2(x-2)(x+3)(x-3)]
=1/[2(x+3)]