Find the Partial Fraction Decomposition for the Rational Expression $$\frac { 4 x ^ { 3 } - 22 x ^ { 2 } + 33 x - 6 } { ( x - 2 ) ^ { 3 } ( x + 2 ) }$$

question 342

Multiple Choice

Find the partial fraction decomposition for the rational expression.
- $$\frac { 4 x ^ { 3 } - 22 x ^ { 2 } + 33 x - 6 } { ( x - 2 ) ^ { 3 } ( x + 2 ) }$$

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

---

Definitions:

Community Comparison Group

A group of individuals who do not receive the intervention or treatment being studied but are similar in other characteristics to the group that does.

Wyatt Standards

Legal standards established from a case to ensure the humane treatment and rights of mental health patients, including the right to receive individual treatment and care.

Psychiatric Patients

Individuals receiving medical treatment for disorders that affect the mind, emotions, and behavior.

Mental Disorder

A wide range of conditions that affect mood, thinking, and behavior, leading to distress or impairment in functioning.