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Mathematics
Problem
For the rational function
5
x
2
+
1
(
x
−
2
)
3
(
x
+
1
)
\displaystyle \frac{5x^{2}+1}{(x-2)^{3}(x+1)}
(
x
−
2
)
3
(
x
+
1
)
5
x
2
+
1
, which one of the following sets of terms must necessarily appear in its partial–fraction decomposition? a)
A
x
−
2
\dfrac{A}{x-2}
x
−
2
A
b)
A
x
−
2
+
B
(
x
+
1
)
\dfrac{A}{x-2}+\dfrac{B}{(x+1)}
x
−
2
A
+
(
x
+
1
)
B
c)
A
x
−
2
+
B
(
x
−
2
)
2
+
C
(
x
−
2
)
3
\dfrac{A}{x-2}+\dfrac{B}{(x-2)^2}+\dfrac{C}{(x-2)^3}
x
−
2
A
+
(
x
−
2
)
2
B
+
(
x
−
2
)
3
C
d)
A
x
−
2
+
B
(
x
−
2
)
2
\dfrac{A}{x-2}+\dfrac{B}{(x-2)^2}
x
−
2
A
+
(
x
−
2
)
2
B
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