∵a^2-5a+3=0
∴a^2+3=5a
（a-5/2)²+3-25/4=0
（a-5/2)²=13/4
a-5/2=±√13/2
a=(5±√13)/2
1/a=2/(5±√13)=-2/3(5±√13)
a^2 -4a +15/a^2+3
=(a^2 -4a +15)/(a^2+3)
=(a^2 -4a +15)/5a
=(a^2+3+12)/5a-4/5
=(5a+12)/5a-4/5
=1-4/5+12/5a
=1/5-12/5*2/3(5±√13)
=1/5-8/5(5±√13)
=1/5-8±8/5√13
=(-39±8√13)/5