How can you decompose a rational function into partial fractions?

1. Divide if improper: If N(x)/D(x) is an improper fraction [degree of N(x) greater than or equal to degree of D(x)], divide the denominator into the numerator to obtain then apply steps 2,3,4 to the proper rational expression N1(x)/D(x).

2. Factor the denominator: Completely factor the denominator into factors of the form (px+q)^m and (ax^2+bx+c)^n

3. Linear factors: For each factor of the form (px+q)^m, the partial fraction decomposition must include the following sum of m fractions.

4. Quadratic factors: For each factor of the form (ax^2+bx+c)^n, the partial fraction decomposition must include the following sum of n fractions.