express in partial fractions x+2/ (x^-1)^2
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Answer:
Explanation:
The expansion for
x
2
(
x
−
1
)
3
is given by
x
2
(
x
−
1
)
3
=
A
(
x
−
1
)
+
B
(
x
−
1
)
2
+
C
(
x
−
1
)
3
reducing the right member to common denominator we have
x
2
(
x
−
1
)
3
=
A
(
x
−
1
)
2
+
B
(
x
−
1
)
+
C
(
x
−
1
)
3
Equating the numerators we have
x
2
=
A
x
2
+
(
B
−
2
A
)
x
+
A
−
B
+
C
giving the following conditions
⎧
⎪
⎨
⎪
⎩
A
=
1
B
−
2
A
=
0
A
−
B
+
C
=
0
solving for
A
,
B
,
C
we get
x
2
(
x
−
1
)
3
=
1
(
x
−
1
)
+
2
(
x
−
1
)
2
+
1
(
x
−
1
)
3
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