1. The problem statement, all variables and given/known data Expand Using Partial Fractions: f(x) = ( 5x-10 )/ ( (x+1)(x-4) ) Involves Integrating afterwards but I don't think this affects my method. 2. Relevant equations This was a question in my mid semester exam, I got the answer correct but he insists my method is wrong. 3. The attempt at a solution The method I used was to get into the form of: ( 5x-10 )/ ( (x+1)(x-4) ) = A/(x+1) + B/(x-4) then, rearrange to: 5x-10 = A(x-4) + B(x+1) and pick values of x to cancel the factors such as 4 and -1 and solve for A & B. so: 5(4)-10 = B(4+1) → B = 2 5(-1)-10 = A(-1-4) → A = 3 I got this method from high school and have been using it ever since, I also found it clearly stated in the text book we are currently using. After showing him he still insists the text book and I are wrong. His reasoning is that finding A & B for a specific value of x cannot be assumed to work for all x. I don't understand his logic as A & B are constants. Is there any way I can prove this to him? Like a rigorous proof of some sort. Or if I am possibly wrong, can someone explain it to me as he is not good with articulating at all. Thanks in advance for any help :).