How do you split a fraction into partial fractions?

In the exam you will be given a fraction with polynomial numerator and denominator, the denominator will either be factored or factorable. Firstly, you need to factorize the denominator. Then to write as partial fractions you should write a term with a constant numerator (A,B,...) for each factor of the denominator. For example, if you were given the fraction (x+3)/x*(x+1) you should write (x+3)/x*(x+1) = A/x + B/(x+1). Then, multiply through by the factorized denominator and expand the brackets on the right hand side, eg. x+3 = A*(x+1) + Bx. You can compare the coefficients to work out the values of the constants (A,B,...). Then simply write the answer, (x+3)/x(x+1) = 3/x + -2/(x+1). There are several pitfalls that can be tricky when dealing with partial fractions. For example this method will not work if the fraction is top heavy (ie. the numerator is of a greater degree than the denominator). When this situation occurs you should use long division to simplify the top heavy fraction first. Additionally, if there is a squared factor in the denominator you should include two terms in the right hand side with different constants. One term with the factor as the denominator, one term with the factor squared in the denominator.