已知x²+y²+6x-8x+25=0,求（x/x²-y² - 1/x+y）÷y/y-x

已知x²+y²+6x-8x+25=0,求（x/x²-y² - 1/x+y）÷y/y-x
已知x²+y²+6x-8x+25=0,求（x/x²-y² - 1/x+y）÷y/y-x

已知x²+y²+6x-8x+25=0,求（x/x²-y² - 1/x+y）÷y/y-x
即(x²+6x+9)+(y²-8y+16)=0
(x+3)²+(y-4)²=0
所以x=-3,y=4
原式=[x-(x-y)]/(x+y)(x-y)*[-(x-y)/y]
=y/(x+y)(x-y)*[-(x-y)/y]
=-1/(x+y)
=-1/(-3+4)
=-1

x²+y²+6x-8x+25=0
(x²+6x+9)+(y²-8x+16)=0
(x+3)²+(y-4)²=0
所以，x=-3,y=4
x/x²-y² - 1/x+y）÷y/y-x
=[x/(x²-y²) - (x-y)/（x+y）（x-y）](y-x)/y
=y/(x²-y²)*(y-x)/y
=-(x+y)
=-1