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Algebra

Ratios with algebra

You remember a thing or two about ratios and proportions from you pre-algebra days. Well, how can we use these same ideas to solve problems in algebra. This tutorial re-introduces ratios in an algebraic context and helps us solve some awesome problems!

Simplifying rational expressions

You get a rational expression when you divide one polynomial by another. If you have a good understanding of factoring quadratics, you'll be able to apply this skill here to help realize where a rational expression may not be defined and how we can go about simplifying it.

Rational expressions and equations

Have you ever wondered what would happen if you divide one polynomial by another? What if you set that equal to something else? Would it be as unbelievably epic as you suspect it would be? Well, rational expressions are just algebraic expressions formed by dividing one expression by another. We get a rational equation if we set that equal to something else. In this tutorial, we work through examples to understand and apply rational expressions and equations.

Graphing rational functions

Rational functions are often not defined at certain points and have very interesting behavior has the input variable becomes very large in magnitude. This tutorial explores how to graph these functions, paying attention to these special features. We'll talk a lot about vertical and horizontal asymptotes.

Partial fraction expansion

If you add several rational expressions with lower degree denominator, you are likely to get a sum with a higher degree denominator (which is the least-common multiple of the lower-degree ones). This tutorial lets us think about going the other way--start with a rational expression with a higher degree denominator and break it up as the sum of simpler rational expressions.

Solving rational equations

The equations you are about to see are some of the hairiest in all of algebra. The key is to keep calm and don't let the rational equation be the boss of you.