Evaluate ∆2(1/(x2+5x+6), taking h=1
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Answer:
Factorize the denominator:
x
2
−
5
x
+
6
=
(
x
−
2
)
(
x
−
3
)
Before performing partial fraction decomposition of the rational function, the numerator must have lower degree than the denominator, so split the function as:
x
2
+
8
x
2
−
5
x
+
6
=
x
2
−
5
x
+
6
+
5
x
+
2
x
2
−
5
x
+
6
=
1
+
5
x
+
2
x
2
−
5
x
+
6
Now:
5
x
+
2
x
2
−
5
x
+
6
=
A
x
−
2
+
B
x
−
3
5
x
+
2
x
2
−
5
x
+
6
=
A
(
x
−
3
)
+
B
(
x
−
2
)
(
x
−
2
)
(
x
−
3
)
5
x
+
2
=
A
x
−
3
A
+
B
x
−
2
B
5
x
+
2
=
(
A
+
B
)
x
−
(
3
A
+
2
B
)
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