What term(s) should appear in the partial fraction decomposition of a proper rational function with each of the following? a. A factor of x-3 in the denominator b. A factor of (x-4)³ in the denominator c. A factor of x² + 2x + 6 in the denominator

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.6: Partial Fractions
Problem 51E
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What term(s) should appear in the partial fraction decomposition of a proper rational function with each of the following?
a. A factor of x-3 in the denominator
b. A factor of (x-4)³ in the denominator
c. A factor of x² + 2x + 6 in the denominator
c. When a proper rational function has factor of x + 2x + 6 in the denominator, which of the following should appear in its partial fraction decomposition? Choose the correct answer below.
OA.
O. C.
Ax
x²+2x+6
A₁
B. x²+2x+6x²+2x+6
O D.
A
x²+2x+6
A₂
Ax+ B
x²+2x+6
Transcribed Image Text:What term(s) should appear in the partial fraction decomposition of a proper rational function with each of the following? a. A factor of x-3 in the denominator b. A factor of (x-4)³ in the denominator c. A factor of x² + 2x + 6 in the denominator c. When a proper rational function has factor of x + 2x + 6 in the denominator, which of the following should appear in its partial fraction decomposition? Choose the correct answer below. OA. O. C. Ax x²+2x+6 A₁ B. x²+2x+6x²+2x+6 O D. A x²+2x+6 A₂ Ax+ B x²+2x+6
What term(s) should appear in the partial fraction decomposition of a proper rational function with each of the following?
a. A factor of x-3 in the denominator
b. A factor of (x-4)³ in the denominator
c. A factor of x² + 2x+6 in the denominator
a. When a proper rational function has factor of x-3 in the denominator, which of the following should appear in its partial fraction decomposition? Choose the correct answer below.
Ax
x-3
OA.
B.
C.
) D.
A
x-3
Ax
A
x-3' x-3
A₁
A₂
x-3' x-3
Transcribed Image Text:What term(s) should appear in the partial fraction decomposition of a proper rational function with each of the following? a. A factor of x-3 in the denominator b. A factor of (x-4)³ in the denominator c. A factor of x² + 2x+6 in the denominator a. When a proper rational function has factor of x-3 in the denominator, which of the following should appear in its partial fraction decomposition? Choose the correct answer below. Ax x-3 OA. B. C. ) D. A x-3 Ax A x-3' x-3 A₁ A₂ x-3' x-3
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