∵x²+y²-2x-y+5/4
=(x²-2x+1)+(y²-y+1/4)
=(x-1)²+(y-1/2)²
=0
又∵(x-1)²和(y-1/2)²均≥0
∴x-1=0,y-1/2=0
∴x=1,y=1/2
∴xy/(x+y)
=1×1/2÷(1+1/2)
=1/3