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.

State how you can solve a system of two equations with two unknowns.

1. Solve for one variable in terms of the other in either equation.
2. Substitute this in the other equation, and solve for the other variable.
3. Substitute this back in the equation obtained in step 1 to find the variable.
4. Check by plugging in the original equation.