作业帮已知:x^2+y^2+6x-8y+25=0,求(x/x^2-y^2)÷y/(y-x)
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已知:x^2+y^2+6x-8y+25=0,求(x/x^2-y^2)÷y/(y-x)
已知:x^2+y^2+6x-8y+25=0,求(x/x^2-y^2)÷y/(y-x)
已知:x^2+y^2+6x-8y+25=0,求(x/x^2-y^2)÷y/(y-x)
x²+y²+6x-8y+25=0
(x²+6x+9)+(y²-8y+16)=0
(x+3)²+(y-4)²=0
x+3=0,y-4=0
x=-3,y=4
x/(x²-y²)÷y/(y-x)
=x/[(x+y)(x-y)]×(y-x)/y
=-x/[y(x+y)]
=3/[4×(-3+4)]
=3/4
即(x²+6x+9)+(y²-8y+16)=0
(x+3)²+(y-4)²=0
所以x+3=0，y-4=0
所以x=-3,y=4
所以原式=x/(x+y)(x-y)*[-(x-y)/y]
=-x/[y(x+y)]
=3/[4*(-3+4)]
=3/4
x^2+y^2+6x-8y+25=0
（x+3）²+（y-4）²=0
x+3=0，y-4=0
所以x=-3，y=4
x/(x^2-y^2)÷y/(y-x)
=x/(x+y)(x-y)×(y-x)/y
= -x/y(x+y)
=3/[4×（-3+4）]
=3/4
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