Partial Fractions

A given proper fraction can be expressed as the sum of other simple fractions corresponding to the factors of the denominator of the given proper fraction. This process is called splitting into Partial Fractions.

If the given fraction p(x)/q(x) is improper then convert into sum of a polynomial expression and a proper rational fraction by dividing p(x) by q(x).

A proper fraction is one in which the degree of the numerator is less than the degree of the denominator. An improper fraction is a fraction in which the degree of the numerator is greater than or equal to the degree of the denominator.

Types of Partial Fractions

Type 1: Linear factors, none of which is repeated

Type 2: Linear factors, some of which are repeated

Type 3: Quadratic factors, none of which is repeated