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Mathematics
Problem
For constants
A
,
B
,
C
,
D
,
E
A,B,C,D,E
A
,
B
,
C
,
D
,
E
the identity
3
x
3
+
5
x
2
+
2
(
x
−
1
)
(
x
2
+
1
)
2
=
A
x
−
1
+
B
x
+
C
x
2
+
1
+
D
x
+
E
(
x
2
+
1
)
2
\frac{3x^{3}+5x^{2}+2}{(x-1)(x^{2}+1)^{2}}=\frac{A}{x-1}+\frac{Bx+C}{x^{2}+1}+\frac{Dx+E}{(x^{2}+1)^{2}}
(
x
−
1
)
(
x
2
+
1
)
2
3
x
3
+
5
x
2
+
2
=
x
−
1
A
+
x
2
+
1
B
x
+
C
+
(
x
2
+
1
)
2
D
x
+
E
holds for all real
x
x
x
. What is the value of
C
C
C
? a)
−
3
2
-\dfrac32
−
2
3
b) \dfrac12 c) \dfrac32 d) -\dfrac12
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