a是方程x^2-3x+1=0的根
a^2-3a+1=0
所以a^2-3a=-1
且a^2+1=3a
所以
2a^2-5a-2+3/(a^2+1)
=2a^2-6a+a-2+3/(3a)
=2(a^2-3a)+a-2+1/a
=2*(-1)+a-2+1/a
=a-3+1/a
=(a^2-3a+1)/a
=0/a
=0