Partial fraction decomposition is a method used in mathematics and engineering to simplify a rational function into several simple fractions. This allows for easier integration, differentiation, and other calculations.
Partial fraction decomposition is useful because it allows for simpler manipulation and calculations of rational functions. It also allows for solving more complex equations and systems of equations.
The process of partial fraction decomposition involves finding the partial fractions that make up a rational function by equating the coefficients of the terms in the numerator and denominator. This can be done using algebraic manipulation and solving a system of equations.
Partial fraction decomposition can be applied to any proper rational function, which is a function in the form of p(x)/q(x) where the degree of the numerator is less than the degree of the denominator.
There are certain limitations and restrictions when using partial fraction decomposition. The rational function must be proper, and the denominator must be factorable into linear and/or irreducible quadratic terms. Additionally, complex roots must be included in the decomposition if they are present in the original function.