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Complex Fractions: Technicalities

I started with:

  • Simplify the following expression:
    • [ (y / x) - (x / y) ] / [ (x + y) / xy ]

...and ended up with:   Copyright Elizabeth Stapel 2003-2011 All Rights Reserved

      y - x, for neither x nor y equal to zero and x not equal to -y

The restriction at zero is easy to understand, but what about the other? For this complex fraction to be defined, the denominator fraction can't be zero. To get the denominator fraction equal to zero, I would have to have x + y = 0, or x = y.

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