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Mathematics
Problem
Which of the following is the correct partial–fraction form of the proper rational function
3
x
+
2
x
2
+
4
x
+
5
\dfrac{3x+2}{x^{2}+4x+5}
x
2
+
4
x
+
5
3
x
+
2
? a)
A
x
2
+
4
x
+
5
\dfrac{A}{x^{2}+4x+5}
x
2
+
4
x
+
5
A
b)
A
x
+
1
+
B
x
+
4
\dfrac{A}{x+1}+\dfrac{B}{x+4}
x
+
1
A
+
x
+
4
B
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
+
2
+
B
(
x
+
2
)
2
+
1
\dfrac{A}{x+2}+\dfrac{B}{(x+2)^{2}+1}
x
+
2
A
+
(
x
+
2
)
2
+
1
B
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