Complex Fractions: Technicalities
Purplemath
On the referring page, I had started with the following exercise:
- Simplify the following expression:
![[ (y / x) - (x / y) ] / [ (x + y) / xy ]](rational/compfr07.gif)
And I'd ended up with this answer:
The restrictions at zero are easy to understand — if either of x and y were zero, then I'd have created a division by zero, which is forbidden — but what about the other restriction?
For this complex fraction to be defined, the denominator of the entire fraction can't be zero. To get the denominator fraction equal to zero, I would have to have its numerator, namely, x + y, equal 0. And means the same thing as x = −y.
Or, if you don't want to try to check all of these options, then just keep careful track of whatever is cancelled off. In the last step before I finally arrived at my answer, I had cancelled off duplicate factors of x + y. Taking this into account (by setting it equal to zero and solving) gives me that third restriction.
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