Find Partial Fraction Expansion
The Attempt at a Solution
10/[s (s+2)(s+3)^2] = A/s + B/(s+2) + C/(s+3)^2 + D/(s+3)
A = 10/[(s+2)(s+3)^2], s approaches 0 = 10/(2*3^2) = 5/9
B = 10/[s (s+3)^2], s approaches -2 = 10/(-2) = -5
C = 10/[s (s+2)], s approaches -3 = 10/[(-3)(-3+2)] = 10/[(-3)(-1)] = 10/3
First I find the equation that isolated C by multiply both sides by (s+3)^2
10/[s (s+2)] = [A(s+3)^2]/s + [B(s+3)^2]/(s+2) + C + D(s+3)
I then differentiate both sides with respect to s to find D? I have solved similar problems before with three terms, one repeated root, and to find the last constant I had to something similar to above and then differentiate both sides, but that doesn't seem to work in this case with four terms, one repeated root.
Any help would be appreciated thanks.