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Complex Fractions: Technicalities

I started with:

  • Simplify the following expression:

      • [ 3 + 9/(x - 3) ] / [ 4 + 12/(x - 3) ]

...and ended up with:   Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved

      3/4 for x not equal to 3

The "x not equal to 3" restriction is easy to understand. The other restriction comes from looking at the whole denominator of the complex fraction:

    4 + 12/(x - 3) = 4x/(x - 3)

This fraction will be zero (and thus the complex fraction will be undefined) when 4x = 0, so x cannot equal 0.

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