a^2-3a+1=0,a^2+1=3a,a+1/a=3,a^2+1/a^2=7
a^3/(a^6+1)=1/(a^3+1/a^3)=1/[(a+1/a)(a^2+1/a^2-1)]=1/[3(7-1)]=1/18