Write the Form of the Partial Fraction Decomposition for the Following

question 127

Multiple Choice

Write the form of the partial fraction decomposition for the following rational expression. $\frac { 7 x - 6 } { x \left( x ^ { 2 } + 10 \right) ^ { 2 } }$

• A) \(\frac { A } { x } + \frac { B x + C } { \left( x ^ { 2 } + 10 \right) ^ { 2 } }\)
• B)\(\frac { A } { x } + \frac { B } { x ^ { 2 } + 10 } + \frac { C } { \left( x ^ { 2 } + 10 \right) ^ { 2 } }\)
• C) \(\frac { A } { x } + \frac { B } { x + 10 } + \frac { C } { x - 10 }\)
• D) \(\frac { A } { x } + \frac { B } { x + 10 } + \frac { C } { ( x + 10 ) ^ { 2 } } + \frac { D } { x - 10 } + \frac { E } { ( x - 10 ) ^ { 2 } }\)
• E)\(\frac { A } { x } + \frac { B x + C } { x ^ { 2 } + 10 } + \frac { D x + E } { \left( x ^ { 2 } + 10 \right) ^ { 2 } }\)

---

Definitions:

Decentralized System

An organizational or technological system where decision-making power and control are distributed away from a central authority.

Bureaucratic Structure

An organizational structure characterized by formal procedures, hierarchy, and clear division of labor.

Authority-And-Responsibility

Concerns the distribution of tasks and the accompanying expectation of accountabilities within an organization, ensuring that individuals have the rights and obligations to execute their roles.

Scalar Principle

An organizational principle that outlines a clear and direct line of authority in the hierarchy from the top of the organization to the lowest level.