Find the Partial Fraction Decomposition for the Rational Expression $$\frac { 6 x ^ { 3 } - 33 x ^ { 2 } + 51 x - 13 } { ( x - 2 ) ^ { 3 } ( x + 3 ) }$$

question 384

Multiple Choice

Find the partial fraction decomposition for the rational expression.
- $$\frac { 6 x ^ { 3 } - 33 x ^ { 2 } + 51 x - 13 } { ( x - 2 ) ^ { 3 } ( x + 3 ) }$$

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

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