Find the Partial Fraction Decomposition for the Rational Expression $\frac { - 5 x ^ { 2 } - 9 x + 11 } { ( x + 4 ) ^ { 2 } ( 3 x + 1 ) }$

question 1

Multiple Choice

Find the partial fraction decomposition for the rational expression.
$\frac { - 5 x ^ { 2 } - 9 x + 11 } { ( x + 4 ) ^ { 2 } ( 3 x + 1 ) }$

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

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