Factor the Denominator of the Given Rational Expression, and Then $\frac { 2 x ^ { 3 } + 11 x - 3 } { x ^ { 4 } + 6 x ^ { 2 } + 9 }$

question 11

Multiple Choice

Factor the denominator of the given rational expression, and then find the partial fraction decomposition. $\frac { 2 x ^ { 3 } + 11 x - 3 } { x ^ { 4 } + 6 x ^ { 2 } + 9 }$

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

---

Definitions:

Eating Meals

The habitual process of consuming food in structured intervals throughout the day to meet nutritional needs and maintain health.

Eating Out

The activity of dining in restaurants or outside the home, often associated with socializing, convenience, or experiencing new foods.

Lapse

A temporary failure to maintain a higher state of wellness or achievement, often seen as a brief return to previous unhealthy behaviors.

High-Risk Situation

Circumstances or environments that have an increased likelihood of leading to negative or undesired outcomes.