Given that x is ^ 2 + y ^ 2-6x-8y + 25 = 0, find 1 / X-Y / x + Y / x ^ 4-y ^ 4

Given that x is ^ 2 + y ^ 2-6x-8y + 25 = 0, find 1 / X-Y / x + Y / x ^ 4-y ^ 4

x^2+y^2-6x-8y+25=0
x^2-6x+9 +y^2-8y+16=0
(x-3)^2 + (y-4)^2=0
∴x=3,y=4
I can't see what the polynomial you asked for is, but when I know the values of X and y, the result is easy to get

Known: x ^ 2 + y ^ 2 + 6x-8y + 25 = 0, find (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

Given that x ^ 2 + y ^ 2-6x-8y + 25 = 0, find y of X-Y of X

x^2+y^2-6x-8y+25=0
(x-3)^2+(y-4)^2=0
x=3,y=4
y/x-x/y
=4/3-3/4
=7/12