document.write( "Question 896719: What is the value of x+y/y-x if x=m+n/m-n and y=m-n/m+n ? \n" ); document.write( "

Algebra.Com's Answer #543732 by KMST(5328) $\"\"$ $\"About$

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.
\n" ); document.write( "x+y/y-x = $\"x%2By%2Fy-x\"$ =x+1-x=1
\n" ); document.write( "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.
\n" ); document.write( "You probably meant to ask about the value of
\n" ); document.write( "(x+y)/(y-x) = $\"+%28x%2By%29%2F%28y-x%29\"$
\n" ); document.write( "when
\n" ); document.write( " $\"x=%28m%2Bn%29%2F%28m-n%29\"$ and $\"y=%28m-n%29%2F%28m%2Bn%29\"$
\n" ); document.write( "
\n" ); document.write( "If you are typing on one line of text, you need those parentheses.
\n" ); document.write( "
\n" ); document.write( "With $\"x=%28m%2Bn%29%2F%28m-n%29\"$ and $\"y=%28m-n%29%2F%28m%2Bn%29\"$ ,
\n" ); document.write( "it is clear that $\"xy=1\"$ <---> $\"y=1%2Fx\"$ ,
\n" ); document.write( "and substituting gives you
\n" ); document.write( " $\"%28x%2By%29%2F%28y-x%29=%28x%2B1%2Fx%29%2F%281%2Fx-x%29=%28x%5E2%2B1%29%2F%281-x%5E2%29\"$
\n" ); document.write( "That can be written in other forms,
\n" ); document.write( "either based on $\"x\"$ , or based on $\"m\"$ and $\"n\"$ .
\n" ); document.write( "You could even have used $\"xy=1\"$ <---> $\"x=1%2Fy\"$ to substitute into $\"%28x%2By%29%2F%28y-x%29\"$ ,
\n" ); document.write( "and we would have ended with an expression based on $\"y\"$ .
\n" ); document.write( "Any way, you do not end with a constant value. \n" ); document.write( "

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