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Ledge
- 4
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Homework Statement
Expand Using Partial Fractions:
f(x) = ( 5x-10 )/ ( (x+1)(x-4) )
Involves Integrating afterwards but I don't think this affects my method.
Homework Equations
This was a question in my mid semester exam, I got the answer correct but he insists my method is wrong.
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 textbook we are currently using. After showing him he still insists the textbook 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 :).