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Mathematics
Problem
Which of the following represents the correct general partial-fraction decomposition of
x
2
(
x
−
1
)
(
x
2
+
1
)
\dfrac{x^{2}}{(x-1)(x^{2}+1)}
(
x
−
1
)
(
x
2
+
1
)
x
2
? a)
A
x
−
1
+
B
x
2
+
1
\dfrac{A}{x-1}+\dfrac{B}{x^{2}+1}
x
−
1
A
+
x
2
+
1
B
b)
A
x
−
1
+
B
x
+
C
x
2
+
1
\dfrac{A}{x-1}+\dfrac{Bx+C}{x^{2}+1}
x
−
1
A
+
x
2
+
1
B
x
+
C
c)
A
x
−
1
+
B
x
+
C
(
x
2
+
1
)
2
\dfrac{A}{x-1}+\dfrac{Bx+C}{(x^{2}+1)^{2}}
x
−
1
A
+
(
x
2
+
1
)
2
B
x
+
C
d)
A
(
x
−
1
)
2
+
B
x
+
C
x
2
+
1
\dfrac{A}{(x-1)^{2}}+\dfrac{Bx+C}{x^{2}+1}
(
x
−
1
)
2
A
+
x
2
+
1
B
x
+
C
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