Page 64 - LAPLACE TRANSFORM

3.2 PARTIAL FRACTION

Be warned that in my class I’ve got a rule that if the denominator can be factored
with integer coefficients, then it must be.

So, let’s remind you how to get the correct partial fraction decomposition. The first
step is to factor the denominator as much as possible. Then for each term in the
denominator we will use the following table to get a term or terms for our partial
fraction decomposition.

Notice that the first and third cases are really special cases of the second and fourth
cases respectively.

3.2.1 Table Of Partial Fractions

Partial Fraction
Type Form of Rational Fraction
Decomposition

Linear Factor (px + q)/(ax + b) A/(ax + b)

Repeated Linear n A1/(ax + b) + A2/(ax +
2
n
Factor (px + q)/(ax + b) b) + .......... An/(ax + b)

2
2
2
Quadratic Factor (px + qx + r)/(ax + bx + c) (Ax + B)/(ax + bx + c)
(A1x + B1)/(ax + bx + c) +
2
2
Repeated 2 2 n (A2x + B2)/(ax + bx +
2
2
Quadratic Factor (px + qx + r)/(ax + bx + c) c) + ...(Anx + Bn)/(ax +
n
bx + c)

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