A) (a^2+3)/(a^3-3-a)/(3a) = (a^2+3)/(a^2-4)/(3a) = (a^2+3)/(a-2)(a+2)/(3a)
= (a^2+3)/(3a)(a-2)(a+2)

B) (x)/(x-1) + (x)/(x+1)
= [(x)(x+1) + (x)(x-1)] / [(x-1)(x+1)]
= (x^2 + x + x^2 - x) / (x^2 - 1)
= (2x^2) / (x^2 - 1)