Answers and Explanations 557
Answers
901–1,001
940.
A
x
B
x
C
x
D
x
E
x
+
+
+
+
+
+
2
3
2
1
1
(
) (
)
The given expression is
4
1
1
3
2
x
x x
+
+
(
)
Notice that you have the linear factor x raised to the third power and the linear factor
(x + 1) raised to the second power. Therefore, in the decomposition, all the numerators
will be constants:
4
1
1
1
1
3
2
2
3
2
x
x x
A
x
B
x
C
x
D
x
E
x
+
+
= +
+
+
+
+
+
(
)
(
) (
)
941.
A
x
B
x
Cx D
x
−
+ +
+
+
+
1
1
1
2
The given expression is
2
1
4
x
x −
Begin by factoring the denominator completely:
2
1
2
1
1
2
1
1
1
4
2
2
2
x
x
x
x
x
x
x
x
x
−
=
−
(
) +
(
)
=
−
+
+
(
)
(
)(
)
In this expression, you have two distinct linear factors and one irreducible quadratic
factor. Therefore, the fraction decomposition becomes
2
1
1
1
1
1
1
2
2
x
x
x
x
A
x
B
x
Cx D
x
(
)(
)
−
+
+
(
)
= −
+ +
+
+
+
942.
A
x
B
x
Cx D
x
Ex F
x
Gx H
x
+
+
+
(
)
+
+
+
+
+
+
(
)
+
+
+
(
)
1
1
5
5
5
2
2
2
2
2
3
Here’s the given expression:
5
4
1
5
2
2
2
3
x
x
x
x
+ −
+
+
(
)
(
)
In this expression, a linear factor is being squared, and an irreducible quadratic factor
is raised to the third power. Therefore, the fraction decomposition becomes
5
4
1
5
1
1
5
5
2
2
2
3
2
2
2
2
x
x
x
x
A
x
B
x
Cx D
x
Ex F
x
Gx
+ −
+
(
)
+
(
)
= +
+
+
(
)
+
+
+
+
+
+
(
)
+
+ H H
x
2
3
5
+
(
)
943.
A
x
B
x
C
x
D
x
E
x
Fx G
x
+
+
−
(
)
+
−
(
)
+
−
(
)
+
+
+
2
2
3
2
1
1
1
17
The given expression is
4
19
1
1 7
3
2
3
2
x
x x
x
+
−
+
(
)
(
)