1. The form of the partial fractions expansion of the rational function Az - B OA. OB. (2) + + OC. None of these OD. 4 OE. Az | B (²-4) Cz+D T²191145 B (1-2) + + C₂ | D z² 1921-45 (24)² Cz+D 1291145 Cz-D ²19x145 (z²+9+45)(z-4)² 1 where A, B, C, D are contants, is:
1. The form of the partial fractions expansion of the rational function Az - B OA. OB. (2) + + OC. None of these OD. 4 OE. Az | B (²-4) Cz+D T²191145 B (1-2) + + C₂ | D z² 1921-45 (24)² Cz+D 1291145 Cz-D ²19x145 (z²+9+45)(z-4)² 1 where A, B, C, D are contants, is:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Question 1:** The form of the partial fractions expansion of the rational function
\[
\frac{x}{(x^2-9x+45)(x-4)^2}
\]
where A, B, C, D are constants, is:
**Options:**
- **A.** \(\frac{Ax+B}{(x-4)^2} + \frac{Cx+D}{9x+45}\)
- **B.** \(\frac{A}{(x-2)} + \frac{B}{(x+2)} + \frac{Cx+D}{x^2+9x+45}\)
- **C.** None of these
- **D.** \(\frac{A}{x-4} + \frac{B}{(x-4)^2} + \frac{Cx+D}{x^2+9x+45}\)
- **E.** \(\frac{Ax+B}{(x^2-4)} + \frac{Cx+D}{x^2+9x+45}\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb2133c9-e1e5-4d56-9c72-044227328930%2F50decc00-9547-41fc-b21a-39e91cede505%2Fvmp8br_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 1:** The form of the partial fractions expansion of the rational function
\[
\frac{x}{(x^2-9x+45)(x-4)^2}
\]
where A, B, C, D are constants, is:
**Options:**
- **A.** \(\frac{Ax+B}{(x-4)^2} + \frac{Cx+D}{9x+45}\)
- **B.** \(\frac{A}{(x-2)} + \frac{B}{(x+2)} + \frac{Cx+D}{x^2+9x+45}\)
- **C.** None of these
- **D.** \(\frac{A}{x-4} + \frac{B}{(x-4)^2} + \frac{Cx+D}{x^2+9x+45}\)
- **E.** \(\frac{Ax+B}{(x^2-4)} + \frac{Cx+D}{x^2+9x+45}\)
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