Question 896719
This is a weird question, and I feel there is a trick, or a misunderstanding or typos. 
x+y/y-x ={{{x+y/y-x}}}=x+1-x=1
That is what you wrote based on the universally agreed upon order of operations convention, but probably that is not what you meant to ask.
You probably meant to ask about the value of
(x+y)/(y-x) ={{{ (x+y)/(y-x)}}}
when
{{{x=(m+n)/(m-n)}}} and {{{y=(m-n)/(m+n)}}}
 
If you are typing on one line of text, you need those parentheses.
 
With {{{x=(m+n)/(m-n)}}} and {{{y=(m-n)/(m+n)}}} ,
it is clear that {{{xy=1}}}<--->{{{y=1/x}}} ,
and substituting gives you
{{{(x+y)/(y-x)=(x+1/x)/(1/x-x)=(x^2+1)/(1-x^2)}}}
That can be written in other forms,
either based on {{{x}}}, or based on {{{m}}} and {{{n}}} .
You could even have used {{{xy=1}}}<--->{{{x=1/y}}} to substitute into {{{(x+y)/(y-x)}}} ,
and we would have ended with an expression based on {{{y}}} .
Any way, you do not end with a constant value.