已知x^2-2x+y^2+6y+10=0,求分式x^2-2xy/xy+y^2的值

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x^2-2x+y^2+6y+10=0,
x^2-2x+1+y^2+6y+9=0,
(x-1)²+(y+3)²=0
∴x-1=0
y+3=0
∴x=1
y=-3
∴(x^2-2xy)/(xy+y^2)=(1+6)/(-3+9)=7/6

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