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Mathematics
Problem
Which one of the following expressions is identically equal to
3
x
3
+
2
x
+
1
(
x
2
+
4
x
+
5
)
2
\dfrac{3x^{3}+2x+1}{(x^{2}+4x+5)^{2}}
(
x
2
+
4
x
+
5
)
2
3
x
3
+
2
x
+
1
? a)
A
x
2
+
4
x
+
5
+
B
(
x
2
+
4
x
+
5
)
2
\dfrac{A}{x^{2}+4x+5}+\dfrac{B}{(x^{2}+4x+5)^{2}}
x
2
+
4
x
+
5
A
+
(
x
2
+
4
x
+
5
)
2
B
b)
A
x
+
B
x
2
+
4
x
+
5
+
C
x
+
D
(
x
2
+
4
x
+
5
)
2
\dfrac{Ax+B}{x^{2}+4x+5}+\dfrac{Cx+D}{(x^{2}+4x+5)^{2}}
x
2
+
4
x
+
5
A
x
+
B
+
(
x
2
+
4
x
+
5
)
2
C
x
+
D
c)
A
x
+
B
x
2
+
4
x
+
5
\dfrac{Ax+B}{x^{2}+4x+5}
x
2
+
4
x
+
5
A
x
+
B
d)
A
x
+
B
x
2
+
4
x
+
5
+
C
(
x
2
+
4
x
+
5
)
2
\dfrac{Ax+B}{x^{2}+4x+5}+\dfrac{C}{(x^{2}+4x+5)^{2}}
x
2
+
4
x
+
5
A
x
+
B
+
(
x
2
+
4
x
+
5
)
2
C
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