Complex Fractions: Technicalities
Purplemath
In the referring page, I'd started with the following exercise statement:
- Simplify the following expression:
![[ 3 + 9/(x - 3) ] / [ 4 + 12/(x - 3) ]](rational/compfr05.gif)
And I'd ended up with an answer of:
The "x not equal to 3" restriction is easy to understand, and was apparent from the beginning; this restriction came from the fractions in the numerator and denominator of the original expression, in which x = 3 would have caused division by zero.
The other restriction comes from looking at what else was cancelled off during the simplification process. In the last few steps, my work was:
In cancelling the x's from the numerator and denominator of the fraction, I'd made another "division by zero" issue disappear. (Don't get me started on what the value of zero divided by zero "should" be. That's another rant for another time.)
In final form, gives no hint that there had been a zero in the denominator. So, for my answer to be complete (in particular, to be completely equal to the original expression), I needed to add the restriction x ≠ 0.
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