Determine the partial fraction expansion for the rational function below (S-1) (²-1)
Determine the partial fraction expansion for the rational function below (S-1) (²-1)
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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![### Partial Fraction Expansion Problem
#### Problem Statement
Determine the partial fraction expansion for the rational function below:
\[ \frac{5s}{(s-1)(s^2-1)} \]
#### Step-by-Step Solution
To solve this, we break the function into simpler fractions.
\[ \frac{5s}{(s-1)(s^2-1)} = \text{[Fill in the blanks with partial fraction components]} \]
To complete the problem, decompose the rational function into partial fractions that can be added together to form the original function.
##### The rational function in terms of partial fractions will have the form:
\[ \frac{5s}{(s-1)(s^2-1)} = \frac{A}{s-1} + \frac{Bs+C}{(s^2-1)} \]
Where \(A\), \(B\), and \(C\) are constants to be determined.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1d700aa-072a-4ff7-be1d-cdca0f10aa9d%2F3e73333a-0254-4f67-a0de-0e82ac3363c0%2Fokqln4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Partial Fraction Expansion Problem
#### Problem Statement
Determine the partial fraction expansion for the rational function below:
\[ \frac{5s}{(s-1)(s^2-1)} \]
#### Step-by-Step Solution
To solve this, we break the function into simpler fractions.
\[ \frac{5s}{(s-1)(s^2-1)} = \text{[Fill in the blanks with partial fraction components]} \]
To complete the problem, decompose the rational function into partial fractions that can be added together to form the original function.
##### The rational function in terms of partial fractions will have the form:
\[ \frac{5s}{(s-1)(s^2-1)} = \frac{A}{s-1} + \frac{Bs+C}{(s^2-1)} \]
Where \(A\), \(B\), and \(C\) are constants to be determined.
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