(adsbygoogle = window.adsbygoogle || []).push({}); 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 :).

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# Homework Help: Partial Fractions, Method of Cancelling

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