# Partial fraction decomposition

##### Intros

###### Lessons

##### Examples

###### Lessons

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

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

**Case 3: Denominator contains irreducible quadratic factors with no repeats**Find the partial fractions of :

$\frac{2x^{2} + 5x + 8}{x^{3} - 8x}$

**Case 4: Denominator contains irreducible quadratic factors with repeats**Find the partial fractions of:

$\frac{3x^{4} + x^{3} + 1}{x(x^{2} + 1)^{2}}$

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

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###### Topic 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.

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