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Mathematics
Mathematics
Problem
Which one of the following is the correct general partial–fraction form of a proper rational function whose denominator is
(
x
−
3
)
3
(x-3)^3
(
x
−
3
)
3
? a)
A
x
−
3
+
B
(
x
−
3
)
3
\dfrac{A}{x-3}+\dfrac{B}{(x-3)^3}
x
−
3
A
+
(
x
−
3
)
3
B
b)
A
(
x
−
3
)
+
B
(
x
−
3
)
3
\dfrac{A(x-3)+B}{(x-3)^3}
(
x
−
3
)
3
A
(
x
−
3
)
+
B
c)
A
x
−
3
+
B
(
x
−
3
)
2
+
C
(
x
−
3
)
3
\dfrac{A}{x-3}+\dfrac{B}{(x-3)^2}+\dfrac{C}{(x-3)^3}
x
−
3
A
+
(
x
−
3
)
2
B
+
(
x
−
3
)
3
C
d)
A
x
−
3
+
B
(
x
−
3
)
2
\dfrac{A}{x-3}+\dfrac{B}{(x-3)^2}
x
−
3
A
+
(
x
−
3
)
2
B
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