How do you express x−1x3+x2 in partial fractions?
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Answered by
0
The answer is
x
−
1
x
3
+
x
2
=
2
x
−
1
x
2
−
2
x
+
1
Explanation:
Some factorisation to start with
x
−
1
x
3
+
x
2
=
x
−
1
(
x
2
)
(
x
+
1
)
=
A
x
+
B
x
2
+
C
x
+
1
=
A
x
(
x
+
1
)
+
B
(
x
+
1
)
+
C
x
2
(
x
2
)
(
x
+
1
)
So now we can solve for
A
,
B
,
and
C
x
−
1
=
A
x
(
x
+
1
)
+
B
(
x
+
1
)
+
C
x
2
let x=-1,
−
2
=
C
⇒
C
=
−
2
Coefficients of
x
2
,
0
=
A
+
C
⇒
A
=
2
Coefficients of
x
,
1
=
A
+
B
⇒
B
=
−
1
And finally, we have
x
−
1
x
3
+
x
2
=
2
x
−
1
x
2
−
2
x
+
1
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