Partial Fraction Expansion is a mathematical technique used to simplify a rational function into smaller, more manageable parts. It involves breaking down a complex fraction into simpler fractions with the same denominator.
Partial Fraction Expansion is useful in solving integration problems, as it can make the integration process easier and more straightforward. It also allows for solving problems involving complex fractions or improper fractions.
Partial Fraction Expansion is done by first factoring the denominator of the rational function. Then, for each factor, a corresponding fraction is added to the partial fraction expansion, with the same factor in the denominator and a constant in the numerator. The constants are then solved for using algebraic manipulation.
The two main types of partial fraction expansion are proper and improper. Proper partial fraction expansion is used when the degree of the numerator is less than the degree of the denominator, while improper partial fraction expansion is used when the degree of the numerator is greater than or equal to the degree of the denominator.
Partial Fraction Expansion can only be applied to rational functions, which means that the numerator and denominator must be polynomials. It also cannot be used if the denominator has repeated factors or complex roots.