1 / (1+m-n) + 1/(1+n-m) = 1
multiply both sides by (1+m-n)(1+n-m)
(1+n-m) + (1+m-n) = (1+m-n)(1+n-m)
2 = 1 + n - m + m + mn - m^2 - n - n^2 + mn
2 = 1 - m^2 - n^2 + 2mn
m^2 - 2mn + n^2 = -1
m^2 - 2mn + n^2 + 1
Answer 1: This is not always true.
But is it sometimes true? Are there any values for m and n that make this true?
quadratic formula
m = (-(-2n) +- sqrt((-2n)^2 - 4(1)(n^2 + 1))) / 2(1)
m = (4n +- sqrt(4n^2 - 4n^2 - 4)) / 2
m = (4n +- sqrt(-4)) / 2
Can't do the square root of a negative number.
No solution.
Answer 2: There are no values* for m and n that make the original equation true.
.
* Ignoring complex math, i, sqrt(-1) and all that. I feel bad enough already for using the quadratic formula to answer a pre-algebra question.