Question :(

a(x - y)  = b(y - x)

ax - ay  = by - bx

ax + bx  = ay + by

x(a + b)  = y(a + b)

x / y  =  (a + b) / (a + b)    =  1

Apply algebra and play with it for a bit.

$a(x-y)=b(y-x)$

$ax-ay=by-bx$

$ax+bx=by+ay$

$x(a+b)=y(a+b)$

$x=y\frac{a+b}{a+b}$

$x=y$

Therefore,

$\frac{x}{y}=1$

Thanks CPhill and Will85237

OK, Solveit....although, technically.....Will beat me to it....!!!!!!