Partial Fractions

Partial fraction decomposition is used to break up a simplified fraction. For example it would turn 3x+2/x^2+x back into its more complicated form 2/x + 1/x+1.  To do this you first check if the fraction is improper and if it is you divide it (more on that later). Then you factor the denominator and if it is a linear equation you set up fractions with coefficients a, b, c etc over the factored parts and if its quadratic you use the coefficients ax+b cx+d etc.  Once you get the fractions you can multiply the equation by the lcd and then group equations by powers of x. After grouping them you equate the coefficients and then solve the systems of equations and substitute the answers you get for the a, b, c coefficients in the set up fraction. Here is an example of partial fraction decomposition.