Final answer:
F(s) can be decomposed into partial fractions as follows: F(s) = 5/s - 20/(s+5) + 15/(s+5)² - 100/s².
Explanation:
To solve F(s), it is first necessary to decompose the given expression into partial fractions. By breaking down F(s) into its constituent parts, it resolves into F(s) = 5/s - 20/(s+5) + 15/(s+5)² - 100/s². This decomposition simplifies the original complex fraction into a more manageable form, making it easier to analyze and manipulate. Each partial fraction represents a specific component of the original function, enabling a clearer understanding of its behavior and properties. This step-by-step breakdown aids in further mathematical operations or analysis that may be required for the given function.
The process of decomposing the expression allows for a more systematic approach to handling complex rational functions, leading to a concise representation that facilitates computations and evaluations. Understanding how the original function breaks down into its constituent parts provides valuable insights into its structure and behavior, aiding in various mathematical applications. This method of decomposition is a fundamental technique used in handling rational functions across different mathematical domains.