1. The problem statement, all variables and given/known data I am given 9/[(s-1)(s-1)(s-4)] as part of a Laplace Transform. I'm supposed to decompose into partial fractions. 2. Relevant equations So 9/[(s-1)(s-1)(s-4)]= D/(s-1)+E/(s-1)+F/(s-4) 3. 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.