LOL Guest #1, you need not do that to me in question #1.
\(\dfrac{(x^{-1}-y^{-1})}{(\pi x-\pi y)(x^2+9\sqrt{\pi}xy+8\pi y^2)}\\ =\dfrac{\frac{y-x}{xy}}{\pi(x-y)(x+\sqrt{\pi}y)(x+8\sqrt{\pi}y)}\\ =-\dfrac{\frac{1}{xy}}{\pi (x+\sqrt{\pi}y)(x+8\sqrt{\pi}y)}\\ = -\dfrac{1}{\pi xy (x+\sqrt{\pi}y)(x+8\sqrt{\pi}y)}\)
You are complexifying that question(Yeah you never heard that word..... I made it up!! :) )