5x(75x+32y)=5xy
375x^2 + 160xy = 5xy
375x^2 = -155xy
375x = -155y
x = -155/375y

(x+y)/(y+x)=xy
(x+y)/(x+y)=xy
1=xy
x=1/y

(x-y)/(y-x)=xy
(x-y)/ -(x-y)=xy
-1=xy
x=-1/y

sqrt(5x)=y
sqrt(5x)^2=y^2
5x=y
x=y/5

(x+y)/(x-y)=2xy
-(y-x)/(x-y)=2xy
-[(y-x)/(x-y)]=2xy
-(-1) = 2xy
x= 1/2y

(1337x)^2-(15y)^2=sqrt(y)
I think your solution to this is correct, so no point in posting

C. M. Ngan
Aerospace Engineering
University of Illinois at Urbana Champaign