Partial Fraction Decomposition Quadratic Factors

In the last lesson, we learned the process of partial fraction decomposition, a technique that allows us to break down a single rational expression into the sum of two or more simpler rational expressions. Our focus was on cases where the denominator consists only of distinct linear factors, making the setup and solution process relatively straightforward. In this lesson, we will take the next step by looking at more complex cases involving distinct quadratic factors as well as repeated quadratic factors in the denominator. While the general approach remains the same, these problems require additional algebraic steps to determine the unknown coefficients, making the solving process more involved. As a result, solving for these unknowns will often require systems of equations or strategic substitution methods.