Partial Fractions Decomposition for 9/[(s-1)(s-1)(s-4)]

[jwang34]

Homework Statement

I am given 9/[(s-1)(s-1)(s-4)] as part of a Laplace Transform. I'm supposed to decompose into partial fractions.

Homework Equations

So 9/[(s-1)(s-1)(s-4)]= D/(s-1)+E/(s-1)+F/(s-4)

The Attempt at a Solution

To simplify:
9= D(s-1)(s-4)+ E(s-1)(s-4)+ F(s-1)^2
So since (s-1)(s-4)=s^2-5s+4
9= Ds^2-5Ds+4D+Es^2-5Es+4E+Fs^2-2Fs+F
So collect like terms
9=(D+E+F)s^2+(-5D-5E-2F)s+4D+4E+F

Now there's three equations and three terms.
D+E+F=0, -5D-5E-2F=0 and 4D+4E+F=9

I have come up with the following D=-1.2, E=4.2, and F=-3 using all three equations but it doesn't satisfy the second equation. I tried to solve this system with a matrix, but that didn't work. I'm wondering if a unique solution even exists...any insight is highly appreciated.

 

[Antineutron]

Homework Equations

So 9/[(s-1)(s-1)(s-4)]= D/(s-1)+E/(s-1)+F/(s-4)

right side is wrong. it should be E/(s-1)^2

 

[rock.freak667]

(s-1)(s-1)(s-4)=(s-1)^2(s-4)

so 9/(s-1)^2(s-4) = A/(s-1)^2 + B/(s-1) + C/(s-4)