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Mathematics
Problem
Decompose the following into the sum of a polynomial and a proper rational function of the form
A
x
+
B
x
2
+
4
x
+
5
\dfrac{Ax+B}{x^2+4x+5}
x
2
+
4
x
+
5
A
x
+
B
:
x
3
+
2
x
2
+
5
x
2
+
4
x
+
5
.
\frac{x^3+2x^2+5}{x^2+4x+5}.
x
2
+
4
x
+
5
x
3
+
2
x
2
+
5
.
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