Partial fraction decomposition  Rational Equations and Expressions
Partial fraction decomposition
Related concepts:
 Integration of rational functions by partial fractions
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?


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

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

5.
First perform long division, then partial fraction decomposition
Find the partial fractions of: