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Mathematics
Problem
For the identity
5
x
−
6
(
x
−
1
)
(
x
+
2
)
(
x
+
3
)
=
A
x
−
1
+
B
x
+
2
+
C
x
+
3
,
\frac{5x-6}{(x-1)(x+2)(x+3)}=\frac{A}{x-1}+\frac{B}{x+2}+\frac{C}{x+3},
(
x
−
1
)
(
x
+
2
)
(
x
+
3
)
5
x
−
6
=
x
−
1
A
+
x
+
2
B
+
x
+
3
C
,
find the value of
A
+
B
+
C
A+B+C
A
+
B
+
C
. a)
−
1
12
-\dfrac{1}{12}
−
12
1
b)
0
0
0
c)
1
1
1
d)
−
5
6
-\dfrac{5}{6}
−
6
5
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