Partial FractionsLinear term to a power on the denominator

Expressions with (ax + b)k in the denominator decompose to terms of the form:

2 3.....

( ) ( )

A B C

ax b ax b ax b

3

8 42

( 3)

x

x

To express

as partial fractions.

2( 3) 3

A B

x x

Express as individual fractions with the factors on the denominator:

2

( 3)

( 3)

A B x

x

Express with a common denominator:

Using Method TwoSubstitution

8 42 ( 3)x A B x Substitute x = 324 – 42 = AA = -18

Now substitute x = 0-42 = -18 - 3BB = 8

2 2

8 42 8 18

( 3) ( 3) ( 3)

x

x x x

Hence: