Analysis and Approaches for IBDP Maths Ebook 2 | Page 55

16
Paper 2 Section A – Partial Fractions Problems
Example
x
(a) Express in partial fractions.
(1 �x
)(3 �x
)
(b)
Hence, by using the extended binomial expansion, find the coefficient of
x
the expansion of .
(1 �x
)(3 �x
)
2
x of
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4
Solution
(a) Let x �
A �
B , where A and B
(1 � x )(3 � x ) 1 � x 3 � x
are constants.
x A(3 �x) B(1 �x)
�
�
(1 � x)(3 � x) (1 � x)(3 � x) (1 � x)(3 � x)
x 3A� Ax � B � Bx
�
(1 � x)(3 � x) (1 � x)(3 � x)
M1
x � ( A� B) x � (3 A� B)
A1
1� A�
B
1�B�
A
0�3A�
B
�0 � 3(1 � B)
� B
A1
0 � 3�3B�
B
�3�
4B
3
B ��
4
� 3 �
� A �1� � � �
� 4 �
1
A �
4
x 1 3
� � �
(1 � x)(3 � x) 4(1 � x) 4(3 � x)
A1
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