x^2+y^2=2x+y-5/4
(x^2-2x+1)+(y^2-y+1/4)=0
(x-1)^2+(y-1/2)^2=0
x=1,y=1/2
所以xy/(x+y)=1*1/2/(1+1/2)=1/2/(3/2)=1/3