We've seen some huge, lumbering polynomials before. Dinosaur-sized polynomials, even, but less extinct. So the idea of putting one polynomial on top of another, to make a rational function, seems terrifying. It's a good thing we know that there's no reason to worry, though; we've messed with rational functions before.
Now we're going to unlock their secrets. No matter how complicated a rational function might appear, it will become very tame and predictable once we figure out where it asymptotes and zeros are. And that is the key to sketching rational functions. That's right; we're drawing them, and it isn't going to be a total pain in the butt. Believe it.