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Mathematics
Problem
For constants
A
,
B
,
C
,
D
A,\,B,\,C,\,D
A
,
B
,
C
,
D
, suppose
3
x
2
+
2
x
−
1
(
x
−
1
)
2
(
x
2
+
4
)
=
A
x
−
1
+
B
(
x
−
1
)
2
+
C
x
+
D
x
2
+
4
.
\frac{3x^{2}+2x-1}{(x-1)^{2}(x^{2}+4)}=\frac{A}{x-1}+\frac{B}{(x-1)^{2}}+\frac{Cx+D}{x^{2}+4}.
(
x
−
1
)
2
(
x
2
+
4
)
3
x
2
+
2
x
−
1
=
x
−
1
A
+
(
x
−
1
)
2
B
+
x
2
+
4
C
x
+
D
.
Which of the following ordered pairs
(
C
,
D
)
(C,D)
(
C
,
D
)
is correct? a)
(
−
32
25
,
46
25
)
\left(-\dfrac{32}{25},\,\dfrac{46}{25}\right)
(
−
25
32
,
25
46
)
b)
(
−
32
25
,
23
25
)
\left(-\dfrac{32}{25},\,\dfrac{23}{25}\right)
(
−
25
32
,
25
23
)
c)
(
32
25
,
23
25
)
\left(\dfrac{32}{25},\,\dfrac{23}{25}\right)
(
25
32
,
25
23
)
d)
(
−
32
25
,
−
23
25
)
\left(-\dfrac{32}{25},\,-\dfrac{23}{25}\right)
(
−
25
32
,
−
25
23
)
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