Partial Fraction Decomposition
Partial Fraction Decomposition
Many rational functions can be expressed as a sum of simpler fractions. For example, can be expressed as the sum +. To find A and B, Heaviside's method can be used. First, multiply the original fraction by , cancel, and substitute 1 for : (x-1)=⇒A==-1. Similarly,
x+1
(x-3)(x-1)
A
x-3
B
x-1
(x-1)
x
x+1
(x-3)(x-1)
x+1
x-3
1+1
1-3
x+1
(x-3)(x-1)
x+1
x-1
3+1
3-1
x+1
(x-3)(x-1)
2
x-3
-1
x-1