In this unit, we'll tie up some 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'll 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'll 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.
Purplemath: Polynomial Long Division
Check this out for a detailed, step-by-step explanation of how to go through a polynomial long division problem. The explanation is even longer than the division, but that's a good thing.
Math is Fun: Rational Expressions
This site will help solidify in your mind everything you've learned about rational expressions, as well as delve into other aspects of rational expressions that you may not be ready for yet. It's like a sneak peek into the great unknown. Bring a sweater in case it gets cold.
Purplemath: Work Word Problems
Another page from the good people at Purplemath, but this one takes you through solving a "Work" Word Problem. In other words, "how long does it take a to accomplish b in c time?" Sorry to hit you with a bunch of variables right out of the gate like that.
eHow: Dividing Polynomials
Are all those numbers, lines, and signs in polynomial division problems making you dizzy? Need someone to visually break it down for you? Enter Jimmy. He'll walk you through a sample problem so you'll feel more at ease doing others on your own. Take it away, Jimmy.
Online Math Learning: Factoring Polynomials
Not one, not two, but three videos to help you get over the factoring polynomials hump! Hm, that was supposed to be funny. So much for the "rule of threes."
YourTutorOnline: Simplify Complex Rational Expressions
Complex = bad. Simple = good. Let this online tutor help you take "bad" expressions and make them "good." And it doesn't even require sending them to military school.
Polymathlove: Free Math Solver
Check out a multitude of rational expressions here, then see how to simplify, factor, or expand them and how to find the GCF or LCM! Keep clicking "New Example" until you've seen enough. Click "Factor," and it will factor things for you! It's like having a math butler!
Hotmath Practice Problems
Practice multiplying and dividing rational expressions, then click on the button to see if you did them right. Although this site is called "Hotmath," we urge you not to fall for it too deeply. It's way out of your league.
Mathportal: Rational Expressions Calculator
Plug in your own numerator and denominator, and let the calculator do the rest. You should probably use it only as a learning tool, however, and not to cheat. You'd have a hard time hiding your entire laptop inside one of your sleeves anyway.