Write the Form of the Partial Fraction Decomposition of the Rational

question 96

Multiple Choice

Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.
$$\frac { x + 9 } { x \left( x ^ { 2 } + 3 \right) ^ { 2 } }$$

• A) \(\frac { A x + B } { x ^ { 2 } + 3 } + \frac { C x + D } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }\)
• B) \(\frac { A } { x } + \frac { B } { x ^ { 2 } + 3 } + \frac { C } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }\)
• C) \(\frac { A } { x } + \frac { B x + C } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }\)
• D) \(\frac { A x + B } { x } + \frac { C x + D } { x ^ { 2 } + 3 } + \frac { E x + F } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }\)
• E) \(\frac { A } { x } + \frac { B x + C } { x ^ { 2 } + 3 } + \frac { D x + E } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }\)

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