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Mathematics
Problem
Which of the following expresses the rational function
3
x
+
5
(
x
−
2
)
(
x
+
1
)
\displaystyle\frac{3x+5}{(x-2)(x+1)}
(
x
−
2
)
(
x
+
1
)
3
x
+
5
as a sum of simpler fractions whose denominators are the linear factors
x
−
2
x-2
x
−
2
and
x
+
1
x+1
x
+
1
? a)
A
x
+
B
x
−
2
+
C
x
+
1
\displaystyle\frac{Ax+B}{x-2}+\frac{C}{x+1}
x
−
2
A
x
+
B
+
x
+
1
C
b)
A
x
−
2
+
B
x
+
1
\displaystyle\frac{A}{x-2}+\frac{B}{x+1}
x
−
2
A
+
x
+
1
B
c)
A
(
x
−
2
)
(
x
+
1
)
+
B
x
+
1
\displaystyle\frac{A}{(x-2)(x+1)}+\frac{B}{x+1}
(
x
−
2
)
(
x
+
1
)
A
+
x
+
1
B
d)
A
x
−
2
+
B
(
x
+
1
)
2
\displaystyle\frac{A}{x-2}+\frac{B}{(x+1)^2}
x
−
2
A
+
(
x
+
1
)
2
B
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