Write the Partial Fraction Decomposition of the Rational Expression $$\frac { 4 x ^ { 3 } + 24 x - 3 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$$

question 135

Multiple Choice

Write the partial fraction decomposition of the rational expression.
- $$\frac { 4 x ^ { 3 } + 24 x - 3 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$$

• A) \(\frac { 4 x } { x ^ { 2 } + 5 } + \frac { 4 x - 3 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }\)
• B) \(\frac { 4 x + 1 } { x ^ { 2 } + 5 } + \frac { 4 x - 3 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }\)
• C) \(\frac { 4 x } { x ^ { 2 } + 5 } + \frac { - 4 x - 3 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }\)
• D) \(\frac { 4 x } { x ^ { 2 } + 5 } + \frac { 4 x + 3 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }\)

---

Definitions:

Right And Wrong

Principles that govern the morality, ethics, and legality of actions or decisions.

Personal Morals

Refers to an individual's set of values and principles that guide their behavior, distinguishing between right and wrong.

Belief System

A set of principles or tenets that together form the basis for a religion, philosophy, or moral outlook.

Professional Ethics

A set of moral principles, standards of behavior, or code of conduct that governs the behaviors of individuals within a specific profession.