x²+y²+5/4=2x+y
x²+y²+1+1/4-2x-y=0
x²-2x+1+y²-y+1/4=0
(x-1)²+(y-1/2)²=0
∴x-1=0 y-1/2=0
x=1 y=1/2
∴
xy/（x+y）
=(1×1/2)/(1+1/2)
=(1/2)/(3/2)
=1/3