I have been having trouble of late with partial fraction decomposition. Not so much the maths, but the intuition behind it. What I mean by this, but a question in front of me, I now what procedure to follow to get the answer, but I don't get why you follow the said produced. I will give an example to show what parts I don't understand. Partial fraction decomposition: 8x-42/x^2+3x-18 Factor the denominator: I understand it a quadratic: which gives me 8x-42/(x+6)(x-3) Now this is the part I do not understand: Why do you use A and B, why do they appear? I really cant see the intuition behind this. 8x-42/x^2+3x-18 = A/x+6 + B/x-3 The rest from here I know how to do: find the LCM and the replace x with and number to = one equation to 0 to see find the value for the A or B. I do hope I have put this in the right forum, as is my first time posting maths equation.