Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Of $\displaystyle \frac{1}{4s^{2}-8s}$

I am approaching the partial fraction $$\displaystyle \frac{1}{4s\left(s-2\right)}=\frac{A}{4s}+\frac{B}{s-2},\text{ where }A=-\frac{1}{2},B=\frac{1}{8}$$

Memorizing the table, I have $$\displaystyle f(t)=-\frac{1}{8}+\frac{1}{8}e^{2t}$$

However, the answer seems to be $$\displaystyle \frac{1}{4}e^{t}\sinh{t}$$

How come?

share|cite|improve this question
The two answers agree: just expand $\text{sinh}t$ – awllower Mar 19 '13 at 4:21

$$\frac{1}{4}e^{t}\sinh{(t)} = \frac{1}{4}e^{t}\left(\frac{e^t - e^{-t}}{2}\right)= \frac{e^{2t}}{8} -\frac{1}{8} \\$$
So both the book and you are correct.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.