SOLUTION: What is the value of x+y/y-x if x=m+n/m-n and y=m-n/m+n ?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: What is the value of x+y/y-x if x=m+n/m-n and y=m-n/m+n ?      Log On


   



Question 896719: What is the value of x+y/y-x if x=m+n/m-n and y=m-n/m+n ?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
This is a weird question, and I feel there is a trick, or a misunderstanding or typos.
x+y/y-x =x%2By%2Fy-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) =+%28x%2By%29%2F%28y-x%29
when
x=%28m%2Bn%29%2F%28m-n%29 and y=%28m-n%29%2F%28m%2Bn%29

If you are typing on one line of text, you need those parentheses.

With x=%28m%2Bn%29%2F%28m-n%29 and y=%28m-n%29%2F%28m%2Bn%29 ,
it is clear that xy=1<--->y=1%2Fx ,
and substituting gives you
%28x%2By%29%2F%28y-x%29=%28x%2B1%2Fx%29%2F%281%2Fx-x%29=%28x%5E2%2B1%29%2F%281-x%5E2%29
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%2Fy to substitute into %28x%2By%29%2F%28y-x%29 ,
and we would have ended with an expression based on y .
Any way, you do not end with a constant value.