Write the Partial Fraction Decomposition of the Rational Expression $\frac { 6 x ^ { 3 } + 5 x ^ { 2 } + 32 x + 26 } { \left( x ^ { 2 } + 6 \right) ^ { 3 } }$

question 133

Multiple Choice

Write the partial fraction decomposition of the rational expression.
- $\frac { 6 x ^ { 3 } + 5 x ^ { 2 } + 32 x + 26 } { \left( x ^ { 2 } + 6 \right) ^ { 3 } }$

• A) \(\frac { 6 x - 5 } { \left( x ^ { 2 } + 6 \right) ^ { 2 } } + \frac { - 4 x + 4 } { \left( x ^ { 2 } + 6 \right) ^ { 3 } }\)
• B) \(\frac { 6 x + 5 } { \left( x ^ { 2 } + 6 \right) ^ { 2 } } + \frac { - 4 x - 4 } { \left( x ^ { 2 } + 6 \right) ^ { 3 } }\)
• C) \(\frac { x } { x ^ { 2 } + 6 } + \frac { 6 x + 5 } { \left( x ^ { 2 } + 6 \right) ^ { 2 } } + \frac { - 4 x - 4 } { \left( x ^ { 2 } + 6 \right) ^ { 3 } }\)
• D) \(\frac { x + 1 } { x ^ { 2 } + 6 } + \frac { 6 x + 5 } { \left( x ^ { 2 } + 6 \right) ^ { 2 } } + \frac { - 4 x - 4 } { \left( x ^ { 2 } + 6 \right) ^ { 3 } }\)

---

Definitions:

Shock

A medical condition that occurs when the body is not getting enough blood flow, leading to a lack of oxygen and nutrients critical for cellular function.

Initial Disaster

The first major catastrophic event that triggers a series of responses or crises, often necessitating emergency intervention.

Crisis Intervention Services

Organizations or programs that offer immediate, short-term assistance to individuals experiencing an acute psychological crisis aiming to minimize stress and improve coping mechanisms.

Educational Seminars

Workshops or lectures aimed at providing information and insights on specific topics to enhance knowledge and skills.