If we multiply the numerators and denominators together, we'll find ourselves in a horrible mess and won't be able to do anything. If we factor first, the problem turns into a much less nauseating beast in which several factors can cancel out. Yeah, that second one sounds good.
Example 2
Multiply .
The first thing we do is factor. Then, the problem looks like this:
When we do the multiplication, lots of junk cancels out:
Our final answer is , which isn't that horrible at all. One might even say it's kind of pleasant. Just kidding! (Not kidding.)
Example 3
Find .
First, we factor:
Then we write the polynomial as a fraction by introducing it to a denominator of 1. ("Polynomial, 1, 1, Polynomial. Oh, you've met.")
We change division to multiplication by the reciprocal and do any possible simplifying. Luckily, there's not much in this case.
.
.
, which isn't that horrible at all. One might even say it's kind of pleasant. Just kidding! (Not kidding.)
.
