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Complex Fractions: Technicalities

I started with:

  • Simplify the following expression:
    • [ (1 / t) - 1 ] / [ (1 / t) + 1 ]

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

      (1 - t) / (1 + t) for t not equal to zero or -1

The restriction at zero is easy to see, but what about the other restriction? Look at how the denominator fraction simplifies:

    1/t + 1 = (t + 1)/t

Then the complex fraction will be undefined if t + 1 = 0, or t = 1.

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