Partial fraction with the expoential mathematical constant in the numerator

[rudyx61]

(3*e^(-2s))/(s(s+5))

I was hoping someone could tell me how to find the partial fraction for the above; the answer i ended up with was: (3/5)/s - (3*e^(10))/(s+5) and i went about it by:

(3*e^(-2s))/(s(s+5))=A/s+B/(s+5)
(3*e^(-2s))=A(s+5) + B(s)
set s=-5 and found B=-3*e^(10)/5
set s=0 and found A=3/5

but apparently the answer shown by my teacher was ((3*e^(-2s)/5)((1/s)-(1/(s+5))

Im pretty much puzzled as to how he got this answer

 

[Dick]

(3*e^(-2s))/(s(s+5))

I was hoping someone could tell me how to find the partial fraction for the above; the answer i ended up with was: (3/5)/s - (3*e^(10))/(s+5) and i went about it by:

(3*e^(-2s))/(s(s+5))=A/s+B/(s+5)
(3*e^(-2s))=A(s+5) + B(s)
set s=-5 and found B=-3*e^(10)/5
set s=0 and found A=3/5

but apparently the answer shown by my teacher was ((3*e^(-2s)/5)((1/s)-(1/(s+5))

Im pretty much puzzled as to how he got this answer

You ONLY do partial fractions on 'polynomial' type expressions, like 1/(s*(s+5)). Your teacher took the common factor 3*e^(-2s) out, did the partial fractions on 1/(s*(s+5)) and then restored the common factor.

 

[rudyx61]

oh spent an hour trying to figure it out turns out the answer lies within the basics
thanks a lot for the help