find partial fraction of 2x+3/x2-2x-3
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Step-by-step explanation:
Explanation:
We begin with
−
2
⋅
x
−
3
x
2
−
x
First we factor the bottom to get
−
2
⋅
x
−
3
x
(
x
−
1
)
.
We have a quadratic on the bottom and a linear on the top this means we are looking for something of the form
A
x
−
1
+
B
x
, where
A
and
B
are real numbers.
Starting with
A
x
−
1
+
B
x
, we use fraction addition rules to get
A
⋅
x
x
(
x
−
1
)
+
B
⋅
(
x
−
1
)
x
(
x
−
1
)
=
A
⋅
x
+
B
x
−
B
x
(
x
−
1
)
We set this equal to our equation
(
A
+
B
)
x
−
B
x
(
x
−
1
)
=
−
2
⋅
x
−
3
x
(
x
−
1
)
.
From this we can see that
A
+
B
=
−
2
and
−
B
=
−
3
.
We end up with
B
=
3
and
A
+
3
=
−
2
or
A
=
−
5
.
So we have
−
5
x
−
1
+
3
x
=
−
2
⋅
x
−
3
x
2
−
x
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