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Contents
Improper Fractions
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Improper Fractions
 
Express in partial fractions:
Notice the numerator is in degree 3 and the denominator is in degree 2.
Hence this is an improper fraction.
Improper
fractions as such can be expressed as
There are 2 ways
to solve this question.
Method 1:
Let
From here,
we can tell that A = 1, as coefficient of x3 in
numerator, divided by coefficient of x2 in denominator, is 2/2 = 1.
C and D
can be found by using "cover-up" rule:
= -2
= 3
Use algebraic
identity to find B:
2x3
- x2 - x + 5 = (x + B) (2x + 1) (x
- 2) - 2 (x - 2) + 3 (2x + 1)
Let x =
0,
-2B + 4 + 3 = 5
B = 1
Therefore,
Method 2: Long division
Performing long
division,
Using the result,
 
Using cover-up rule,
A = [ 4(-0.5) + 7] / (-0.5-2)
= -2
B = [ 4(2) + 7] / [ 2(2) + 1]
= 3
Therefore,
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