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x over y minus y over x divided by 1 over y plus 1 over x.

  • algebra - ,

    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

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