a²-3a=-1
∴a²+1=3a
a²-3a+1=0
a-3+1/a=0
a+1/a=3
3a³-9a²+4a+3/(a²+1)
=3a(a²-3a)+4a+1/a
=-3a+4a+1/a
=a+1/a
=3