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Mathematics
Problem
For the rational function
3
x
2
+
5
(
x
−
1
)
2
(
x
+
2
)
\dfrac{3x^{2}+5}{(x-1)^{2}(x+2)}
(
x
−
1
)
2
(
x
+
2
)
3
x
2
+
5
, which of the following is the correct general form of its partial-fraction decomposition? a)
A
x
−
1
+
B
x
+
2
\dfrac{A}{x-1}+\dfrac{B}{x+2}
x
−
1
A
+
x
+
2
B
b)
A
x
−
1
+
B
(
x
−
1
)
2
+
C
x
+
2
\dfrac{A}{x-1}+\dfrac{B}{(x-1)^{2}}+\dfrac{C}{x+2}
x
−
1
A
+
(
x
−
1
)
2
B
+
x
+
2
C
c)
A
x
−
1
+
B
(
x
−
1
)
2
+
C
(
x
+
2
)
2
\dfrac{A}{x-1}+\dfrac{B}{(x-1)^{2}}+\dfrac{C}{(x+2)^{2}}
x
−
1
A
+
(
x
−
1
)
2
B
+
(
x
+
2
)
2
C
d)
A
x
+
B
(
x
−
1
)
2
+
C
x
+
2
\dfrac{Ax+B}{(x-1)^{2}}+\dfrac{C}{x+2}
(
x
−
1
)
2
A
x
+
B
+
x
+
2
C
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