In this unit, we'll tie up loose ends like dividing polynomials. We'll also introduce rational expressions, which are like rational numbers but with one polynomial over another instead of one integer over another. That's a good thing, too, because we hate choosing one integer over another. They're like our mathematical children. We like 37 best, to be honest, but don't tell the others.
When you're dealing with polynomial division and rational expressions, watch out for the critical error of dividing by zero. If you're haunted forever by the phrase "Thou shalt not divide by zero,'' that's okay; in this case, being haunted is actually beneficial to your education. If only all ghosts were as helpful. (We're looking at you, creepy girl in the attic.)
We will also discuss how to solve equations that involve polynomial and rational expressions, as well as word problems that naturally lead to rational expressions. Our conversation will, of course, be accompanied by the chilling refrain of "Thou shalt not divide by zero." It may not be quite as creepy as the raven's "Nevermore," but it will have to do.
As in the world of polynomials, problems involving rational expressions require attention to detail. We're talking at least as much attention to detail as you put into fixing whatever AutoCorrect does to your text messages before you hit "send." If you work slowly and carefully, the problems will take a while but won't be too hard. You've probably had plenty of practice working slowly when you're trying to drag out the last five minutes of each class, anyway.
Hey, we've been there. We know what goes down.