Partial fraction decomposition is a mathematical method used to break down a rational function into simpler fractions. This allows for easier integration and simplification of complex functions.
Partial fraction decomposition is important because it allows for the integration and simplification of complex rational functions, making it easier to solve equations and understand the behavior of functions.
To perform partial fraction decomposition, the rational function is first written in the form of a numerator over a denominator. Then, the denominator is factored into linear and irreducible quadratic factors. Finally, the coefficients of each factor are determined using a system of equations.
Factoring the denominator in partial fraction decomposition allows for the identification of the simpler fractions that make up the original rational function. This makes it easier to integrate and simplify the function.
Partial fraction decomposition is suitable for rational functions, which are functions with polynomials in the numerator and denominator. These functions can be integrated using partial fraction decomposition to simplify and solve equations.
