Partial Fraction Expansion

[simonbramble]

I am trying to refresh my memory on partial fractions. In the attached I have shown an example given in the book. Trouble is, I cannot get their answers to agree with mine. They think A = -1, B = 2, C = 0, D = -0.5, E = 0.5. Does anyone agree with the book and if so, how did you get your answer? I think the book is wrong, but then I have thought that before and always been wrong...

 

[MrAl]

Hi,

What answer did you get?

Here's my answer...
A=-1
B=3/2
C=1
D=-1/2
E=1/2

Using the book values, we cant seem to get the original expression when we expand it, using the above values we can, so the book must be wrong.

Sometimes books are wrong, sometimes it just looks like they are wrong at first. The only way to know for sure is to come up with a test that proves it. By expanding the two results we can find out which one comes out to the original expression. If you didnt get the results above, substitute your values into the new expression and expand it. If you dont get the original expression some way or another, it's probably not correct. If you do, then it's probably correct.

 

[simonbramble]

Hi Mr Al

You are right and the book is wrong. I made an error in my calculations and ended up with C = 0. Now I see the error, I agree with you. The book gives the answer above. I got the question from the following:https://www.math.utah.edu/~gustafso/HeavisideCoverup.pdf.

I thought it was me going slightly mad. Thanks for the sanity check! - Simon

 

[MrAl]

Hi again simon,

Oh you're welcome. I took a look at that paper and saw that he got everything correct except for "Solving the 5x5 system", where somehow he comes up with the wrong answers for B and C. Funny, it's actually simple to use substitution to get the answers.

Also a little funny is that section is titled, "A Failsafe Method" <little chuckle> so i hate to see the non-failsafe method
Im just kidding around here though, everyone makes mistakes now and then, and i do like his approach there.