The success of this lesson hinges upon our mastery of a couple of algebra concepts. For the first Warm-Up problem, you are simply subtracting two rational expressions. Eventually, this lesson will rewind that process as an aide to integration. The second objective of this lesson requires us to complete the square on the denominator of a rational function. For this version of completing the square, we do not add the same number to both sides of an equation. Instead, we are keeping everything on one side of the equation in an act of adding a fancy zero. That is the technique you should employ to write the function below in vertex form. Duration: 8:27

Partial fraction decomposition attempts to undo the addition of two or more rational expressions. This video takes you through that process for the initial Warm-Up exercise and demonstrates how that technique can be used to evaluate the antiderivative of certain rational functions. Duration: 12:05

Ordinarily, the Basic Equation is solved by simply choosing convenient values of x to make one of your numerator values, A, B, C, ..., mathemagically disappear. Sometimes, however, the Basic Equation is too complicated to solve using this method. Allow me to demonstrate how to set up a solve a system of equations by equating the coefficients that will accomplish the same goal. Duration: 6:15? Duration: 5:05

Example 5 presents another straightforward application of partial fraction decomposition. The question is, how will you even know that you need to do such a thing? Duration: 7:35

Example 6 demonstrates the necessary division you must perform on an improper fraction before attempting to decompose your rational function into its partial fractions. Who knows? When you're done, maybe you won't even have to do PFD. Duration: 4:08

On our most complex example yet, we have a quadratic over a cubic. Quick question: What gives you a clue that this problem is a good candidate for PFD? Duration: 10:53

The AP Exam will only require us to use PFD on ration functions with non-repeating linear factors. If you are so inclined, this optional video will demonstrate what to do when you have at least one repeated linear factor. Duration: 5:37

The AP Exam will also not ask you to perform PFD on prime quadratic factors. Watch as Mario shows us how to do it anyway. Duration: 5:58