a^2-3a+1=0,a^2+1=3a,a+1/a=3
3a^3-8a^2+a+3/(a^2+1)
=3a(a^2-3a+1)+a^2-2a+3/(3a)
=a^2-3a+1+a-1+1/a
=a+1/a-1
=3-1
=2