text: Q:
  
  Solving partial fraction equation for 3 unknowns
  
  Suppose I have a fraction as
  $$\frac{1}{s}\frac{1}{s^2-2s+5}$$
  So that:
  $$1 = (A+B)s^2+(C-2A)s+5A$$
  I'm just confused as to how I can solve for $A,B,$ and $C$.  I know if we plug $s=0$ we get $A = \frac{1}{5}$, but what can I do for B and C?
  
  A:
  
  Both sides of the equation are polynomials in $s$ (the LHS just happens to be a constant polynomial), so you can compare coefficients of $s^2$ on both sides. The coefficient of $s^2$ is zero on LHS and $A+B$ on RHS. So $A+B=0$. Do the similar for the coefficient of $s$.
  
  