Partial Fractions

Recap

Recall that in Secondary 2, we learnt about algebraic fractions and how to express the sum of 2 algebraic fractions as an equivalent single fraction.

For example

Overview of Partial Fractions

For this topic, the aim is to convert a single fraction back into the sum of its component partial fractions. In order to do so, we need to do 3 things:

Step 1a) Check if the algebraic fraction is proper or improper.

An algebraic fraction is improper if the degree of the numerator ≥ the degree of the denominator. Use the applet below to check your understanding of an improper algebraic fraction.

If the algebraic fraction is proper, skip to Step 2, otherwise, convert the fraction to a proper fraction using polynomial long division (Step 1b).

Step 2) Express the fraction in its partial fractions form.