A Level Maths Notes: C4 – Partial Fractions Rules
An algebraic fraction is any
expression of the form
where
and
are
sums or products of polynomials or both. An expression of this sort
typically needs to be written in terms of it's partial fractions –
whereis
written as a sum of algebraic fractions - so that it can be
integrated. There are rules which determine which sums of fractions
are allowable.
1. If the degree of the
numerator is greater than or equal to the degree of the denominator,
then first perform long division ofto
reduce the degree of the polynomialto
below that of
2. Factorise
as
far as possible. Each factor
gives
rise to a partial factor
3. Each factor
gives
rise to a sum of partial fractions
4. Each irreducible
factor
gives
rise to a partial fraction
-
notice that the degree of the numerator is one less than the degree
of the denominator.
Example: Express
as
partial fractions.
Example: Express
as
partial fractions.
Example: Express
as
partial fractions.
