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....!!!!!!