(a^3+4b^3+c^3)/[b(a^2+c^2)]
=[(a+c)(a^2+c^2-ac)+4b^3]/[b((a+c)^2-2ac)]
=[2b((a+c)^2-3ac)+4b^3]/[b(4b^2-2ac)]
=[2(4b^2-3ac)+4b^2]/(4b^2-2ac)
=(12b^2-6ac)/(4b^2-2ac)
=3