(6/9-a^2)-(3/12+4a)

You probably mean

6/(9-a^2) - 3/(12+4a)
= 6/[(3-a)(3+a)] - 3/[4(3+a)]
Rewrite with common denominator
= [6*4 - 3*(3-a)]/[4(3-a)(3+a)]
= (15 - 3a)/[4(3-a)(3+a)]
= (3/4)(5-a))/[(3-a)(3+a)]