Inverse Laplace- Partial Fractions with exponential

[ns5032]

Homework Statement

[e^(-2s)] / (s^2+s-2)
Find the inverse Laplace transform.

Homework Equations

The Attempt at a Solution

I know that I can factor the denominator into (s+2)(s-1). Then I tried to use partial fractions to split up the denominator, but I don't know how to do that with an exponential on the top. Thanks for any help!

 

[EngageEngage]

just write it as exp(whatever)*(1/whatever). Then do partial fractions to get exp(whatever)*(?/a + ?/b). You will see that the exponential will be easy to 'invert' back into the time domain as it corresponds to unit step functions (i believe).

 

[Shawj02]

Im stuck in the same boat, but trying to get the partial fraction for "(e^[-s] -e^[-2s])/[(s^2)(s+1)]"

I wasn't too sure what EngageEngage meant.

 

[alchemist]

i am having the same problems! never knew there was any issue with partial fractions involving exponential components.

my question was to get partial fraction from 3e^-2s/(s(s+5)), so i brought down the exponential function to get 3 different fractions with 1/e^2s, 1/s and 1/(s+5).

But it still doesn't work out.