# Partial fraction decomposition

0/1
##### Intros
###### Lessons
1. Introduction to Partial Fraction Decomposition
What is partial fraction decomposition?
0/8
##### Examples
###### Lessons
1. Case 1: Denominator is a product of linear factors with no repeats

Find the partial fractions of:

1. $\frac{x + 7}{(x + 3)(x - 1)}$
2. $\frac{4x + 3}{x^{2} + x}$
2. Case 2: Denominator is a product of linear factors with repeats

Find the partial fractions of :

1. $\frac{3x^{2} - 5}{(x - 2)^{3}}$
2. $\frac{2x - 1}{x^{2} + 10x + 25}$
3. Case 3: Denominator contains irreducible quadratic factors with no repeats

Find the partial fractions of :

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

1. Case 4: Denominator contains irreducible quadratic factors with repeats

Find the partial fractions of:

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

1. First perform long division, then partial fraction decomposition

Find the partial fractions of:

1. $\frac{x^{3} - 3x^{2} + 4x}{x^{2} - 3x 2}$
2. $\frac{2x^{2} + 14x + 24}{x^{2} + 6x - 16}$