Using Linear Partial Fractions
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
Find
A
A
A
in the decomposition
A
x
+
B
x
−
1
=
2
x
+
3
x
(
x
−
1
)
\frac{A}{x} + \frac{B}{x-1} = \frac{2x+3}{x(x-1)}
x
A
+
x
−
1
B
=
x
(
x
−
1
)
2
x
+
3
.
QUESTION
Identify the partial fractions for
7
x
+
9
x
2
+
x
\frac{7x+9}{x^2+x}
x
2
+
x
7
x
+
9
.
QUESTION
Determine the partial fractions for
8
x
x
2
−
2
x
\frac{8x}{x^2-2x}
x
2
−
2
x
8
x
.
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ANSWER
A
x
+
B
x
−
2
\frac{A}{x} + \frac{B}{x-2}
x
A
+
x
−
2
B
. Factor
x
2
−
2
x
=
x
(
x
−
2
)
x^2-2x = x(x-2)
x
2
−
2
x
=
x
(
x
−
2
)
.
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