因为a^2-2006a+1=0 所以a^2+1=2006a
a^2-2005a+2006/(a^2+1)
=a^2-2005a+2006/2006a
=a^2-2005a+1/a
=a-1+1/a
=(a^2-a+1)/a
=2005a/a
=2005