Aplying Laplace transform and solving for Y(s)/X(s) gives you the transfer function that is the same as the impulse response. Evaluating the transfer function for s=jw and taking magnitude and phase gives you the frequency response.
Commenting on your eq:
j^2 =-1
so
(jΩ +2)/[(jΩ)^2 +5jΩ + 4] = (jΩ +2)/[5jΩ + 4-Ω^2]
to get rid of a J you can normalize. That is multiply numerator and denominator by the conjugate.
Usually this is done to eliminate J in the denominator but you can do it in the numerator multipliying by
(jΩ -2)/(jΩ -2)