In the course of working a 2nd order ODE with initial conditions, I ended up with this part of what I needed to get the inverse Laplace transform of:
Now, the textbook did this:
But this is what I did:
These two answers don't look equivalent, but what I did looks like it should work. So, why is it wrong?
How many textbooks on higher math do you come across that are *clearly* written in the first place? Most books on higher math seem to be written in such a way that you already have to know the subject to begin with just to comprehend their explanation - which is rather pointless.
With everything that we do to manipulate the resulting fraction in order to find a set of inverse transforms, this seemed like a natural - and frankly, mild - step.
No, you made it clear the first time that it couldn't be done. The problem was that I didn't know it couldn't be done, it was never explicitly mentioned in regards to this type of situation, and it *appears* that we do a lot worse when we manipulate the fractions the way we normally do, so I never knew this was an issue.
Thank you for helping to clarify.