Write the Partial Fraction Decomposition of the Rational Expression $\frac { 27 - 5 x } { x ( x - 3 ) ^ { 2 } }$

question 1

Multiple Choice

Write the partial fraction decomposition of the rational expression.
- $\frac { 27 - 5 x } { x ( x - 3 ) ^ { 2 } }$

• A) \(\frac { 3 } { x } + \frac { 4 } { x - 3 } + \frac { - 3 } { ( x - 3 ) ^ { 2 } }\)
• B) \(\frac { 3 } { x } + \frac { - 3 } { x - 3 } + \frac { 4 } { ( x - 3 ) ^ { 2 } }\)
• C) \(\frac { - 3 } { x } + \frac { 3 } { x - 3 } + \frac { 4 } { ( x - 3 ) ^ { 2 } }\)
• D) \(\frac { 3 } { x } + \frac { - 3 } { x - 3 } + \frac { 8 } { ( x - 3 ) ^ { 2 } }\)

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Definitions:

Tendency for Attitudes

A predisposition or inclination to respond in a particular way toward certain situations, objects, or people, reflecting underlying beliefs or feelings.

Cognitive Dissonance Theory

A psychological theory that suggests that we experience discomfort or dissonance when our beliefs, ideals, or actions are in conflict, leading to an internal drive to reduce the dissonance.

Belief Perseverance

The finding that once beliefs form, they are resistant to change, even if the information on which they are based is discredited

Effort Justification

A phenomenon whereby individuals rationalize the effort and resources they put into achieving a goal by increasing their appreciation or valuation of the goal, especially when the effort was substantial.