partial fractions linear term to a power
Post on 30-Jun-2015
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Partial fractions with a linear term to a power on the denominator
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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:
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