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Mathematics
Problem
A student writes the following decomposition:
4
x
+
1
(
x
−
2
)
2
(
x
2
+
3
)
=
A
x
−
2
+
B
(
x
−
2
)
2
+
C
x
2
+
3
.
\frac{4x+1}{(x-2)^{2}(x^{2}+3)}=\frac{A}{x-2}+\frac{B}{(x-2)^{2}}+\frac{C}{x^{2}+3}.
(
x
−
2
)
2
(
x
2
+
3
)
4
x
+
1
=
x
−
2
A
+
(
x
−
2
)
2
B
+
x
2
+
3
C
.
Identify the error in this decomposition and write the correct decomposition form.
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