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Contents
Distinct Linear Factors 1 2
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Distinct Linear Factors
Cover-up Rule
There is a
short cut of obtaining A and B in the previous example directly.
This method is known as the "cover-up" rule.
Look
at the identity .
To find A,
cover (x + 5) on the left-hand side of the identity and put in x = -5,
A = [-(-5) -
26] / (-5-2)
= 3
B= (-2-26) / (2+5)
= -4
The answer is the
same as the one obtained by the previous method.
Note that the
cover-up rule can only be used for distinct linear factors.
Example 2:
 Express in partial fractions:
  Let
 .
Using "cover-up" rule,
To find A, substitute x = -0.5,
A = (-0.5 + 11) / (-0.5 + 2)
= 7
To find B, substitute x = -2,
B = (-2 + 11) / [ 2 (-2) + 1]
= -3
Hence,
Example 3:
Express in partial fractions:
Let
Using "cover-up" rule,
= 1
= 2
= -3
Therefore,
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