Partial fraction decomposition
Partial fraction decomposition
Lessons
Notes:
$\bullet$ Partial fraction decomposition expresses a rational function $\frac{f(x)}{g(x)}$, where $f(x)$ and $g(x)$ are polynomials in $x$, as a sum of simpler fractions.
$\bullet$Partial fraction decomposition only applies to proper fractions in which the degree of the numerator is less than that of the denominator.

a)
What is partial fraction decomposition?

b)
When can we perform partial fraction decomposition?


2.
Case 1: Denominator is a product of linear factors with no repeats
Find the partial fractions of:

3.
Case 2: Denominator is a product of linear factors with repeats
Find the partial fractions of :

6.
First perform long division, then partial fraction decomposition
Find the partial fractions of: