# Partial Fractions with e^x on Top

• Dec 9th 2008, 11:42 AM
bumcheekcity
Partial Fractions with e^x on Top
To put it bluntly, how do I go about solving:

$\displaystyle \frac{e^{-10s}}{(s + 3)(s+2)}$

I'm doing a Laplace Transform of the below, and can't work out how to solve the partial fraction I get (i.e. the above partial fraction). I know how to solve partial fractions normally, it's just the $\displaystyle e^{-10s}$ that's giving me trouble.

$\displaystyle x'' + 5x' + 6x(t) = \delta(t-10)$
• Dec 9th 2008, 11:46 AM
Moo
Hello,

$\displaystyle \frac{e^{10s}}{(s+3)(s+2)}=e^{10s} \cdot \left(\frac{1}{(s+3)(s+2)}\right)$

Now you can do the partial fractions decomposition ^^
• Dec 9th 2008, 11:47 AM
bumcheekcity
Interesting. Probably the stupidest I've felt for months now :P

Wait, in which case, I can't factor out $\displaystyle e^{s}$ here:

$\displaystyle \frac{e^{-s} + 2s + 7} {(s+1)^2}$

Is there a general method when you have a non-polynomial function on top?
• Dec 9th 2008, 11:48 AM
Moo
Quote:

Originally Posted by bumcheekcity
Interesting. Probably the stupidest I've felt for months now :P

haha ! it happens to everybody to forget easy stuff ! (Tongueout)