Partial fraction expansion

The  exercise appears under the Algebra II Math Mission. This exercise introduces the technique of partial fraction expansion, also known as partial fraction decomposition.

Types of Problems
There is one type of problem in this exercise:


 * 1) Find the partial fraction decomposition: This problem provides a "combined" sum of two rational expressions. The student is asked to use partial fraction decomposition to "split" the fraction apart.Pfe1.png

Strategies
Knowledge of the process of partial fraction decomposition is encouraged to ensure success on this exercise.
 * 1) Partial fraction expansion and partial fraction decomposition are the same process.
 * 2) After setting up the partial fractions and inserting variables, solving a systems of equations is the standard way to solve for the coefficients.
 * 3) A technique to increase efficiency after setting up the partial fractions is to "plug-in" strategic values for x (namely the solutions to the binomial factors that are the denominators).

Real-life Applications

 * 1) Partial fraction decomposition is used to split rational expressions for easier integration in integral calculus.