Partial Fraction Decomposition

Decomposes a fraction of polynomials into a sum of simpler fractions

Topics

• Cover Up Method

Complex Numbers

$F(s)=\frac{b(s)}{a(s)}=\frac{b_0+b_{1}s+\dots +b_m{s}^m}{a_0+a_{1}s+\dots +a_n{s}^n}=\frac{r_1}{s-{\lambda }_1}+\dots +\frac{r_n}{s-{\lambda }_n}$

• ${\lambda }_1,\dots ,{\lambda }_n$ are the poles of $F$
• $r_1,\dots ,r_n$ are the residues
• ${\lambda }_k={\lambda }_l^{\ast }\leftrightarrow r_k=r_l^{\ast }$