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) \(\frac { 5 x - 3 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } } + \frac { 2 x } { x ^ { 2 } + 3 }\)

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Definitions:

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