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Mathematics
Problem
For the denominator
x
(
x
−
2
)
2
(
x
2
+
4
)
x(x-2)^{2}(x^{2}+4)
x
(
x
−
2
)
2
(
x
2
+
4
)
, the correct general decomposition is a)
A
x
+
B
(
x
−
2
)
2
+
C
x
+
D
x
2
+
4
\dfrac{A}{x}+\dfrac{B}{(x-2)^{2}}+\dfrac{Cx+D}{x^{2}+4}
x
A
+
(
x
−
2
)
2
B
+
x
2
+
4
C
x
+
D
b)
A
x
+
B
x
+
C
x
−
2
+
D
x
2
+
4
\dfrac{A}{x}+\dfrac{Bx+C}{x-2}+\dfrac{D}{x^{2}+4}
x
A
+
x
−
2
B
x
+
C
+
x
2
+
4
D
c)
A
x
+
B
x
−
2
+
C
(
x
−
2
)
2
+
D
x
+
E
x
2
+
4
\dfrac{A}{x}+\dfrac{B}{x-2}+\dfrac{C}{(x-2)^{2}}+\dfrac{Dx+E}{x^{2}+4}
x
A
+
x
−
2
B
+
(
x
−
2
)
2
C
+
x
2
+
4
D
x
+
E
d)
A
x
+
B
x
−
2
+
C
(
x
−
2
)
2
+
D
x
2
+
4
\dfrac{A}{x}+\dfrac{B}{x-2}+\dfrac{C}{(x-2)^{2}}+\dfrac{D}{x^{2}+4}
x
A
+
x
−
2
B
+
(
x
−
2
)
2
C
+
x
2
+
4
D
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