Summary on Partial Fractions - Ryan

Partial Fractions: To change an algebraic fraction into 2 separate fractions.

"A rational function which may be expressed as a sum of separate fractions is said to be resolved into its partial fractions."

There are different methods to deal with Proper fractions or Improper fractions

A Proper fraction is a fraction whose numerator is smaller than its denominator.

An Improper fraction is a fraction whose numerator is larger than its denominator.

If the rational function is a proper fraction:
For every linear or quadratic factor there is a corresponding partial fraction.
For every repeated linear factor there are 2 corresponding partial fractions.

To find the unknown constants you can:
compare coefficients
substitution method


If the rational function is an improper fraction:

You must divide it to obtain a quotient and a proper fraction so you can change the proper fraction into partial fraction form.