Complex Fractions: Technicalities
Purplemath
In the exercise on the referring page, I had started with this:
- Simplify the following expression:
![[ (1 / t) - 1 ] / [ (1 / t) + 1 ]](rational/compfr09.gif){kind=small}
And I had ended up with my answer being:
The restriction at zero is easy to see — if I had allowed t to equal zero, then there would have been plenty of division by zero in the original expression — but what was the source of the other restriction?
There are two ways to arrive at this other restriction; namely, that t ≠ −1. One way is to look at the expression in the denominator of the original fraction. When is this entire expression equal to zero; that is, for what values of t would that denominator cause division by zero for the entire original complex fraction? Let's find out, starting by multiplying through by t:
The other way to arrive at this domain restriction is to look at the denominator of my simplified fraction. This denominator is 1 + t. This expression will be equal to zero — and thus the entire original complex fraction will be undefined — if t + 1 = 0, or t = –1.
© 2024 Purplemath, Inc. All right reserved. Web Design by 