We just started this and I mostly understand it except when it comes to using A, B, C, etc substitution. What I mean is this, here is an exampe. (6x^2+x+1)/(x^2+1)(x-1) = (Ax+B)/(x^2+1) + (C)/(x-1) You then multiply by denominators so you end up with (Ax+B)*(x-1) + (C)*(x^2+1). You multiply and factor and end up with (A+C)x + (-A+B)x + (-B+C). Then you solve the equations for A B and C since (A+C)=6, (-A+B)=1 and (-B+C)=1. But how do you know which denominators to multiply the numerators by? In some problems you end up with 5 or 6 different denominators, and I do not know which ones to multiply the denominators by. In some problems (unlike the one above) it is broken down into 5 or 6 different integrals instead of 2 and if I don't know which ones to multiply out I cannot solve for A, B, C, etc.