algebra
posted by Olivia on .
x over y minus y over x divided by 1 over y plus 1 over x.

Please use numbers or letter symbols, not words, to represent algebraic expressions. They are much easier to work with.
I will assume this is what you mean:
(x/y  y/x)/(1/y + 1/x)
Multiply both numerator and denominator by xy. This will not change the value of the fraction, and leads to:
(x^2  y^2)/(x + y)
Next, factor the numerator and cancel out the (x+y) that will appear in both numerator and denominator.
You should end up with just x  y