Write the Partial Fraction Decomposition of the Rational Expression $\frac { 6 x ^ { 3 } + 4 x ^ { 2 } + 13 x + 15 } { \left( x ^ { 2 } + 3 \right) ^ { 3 } }$

question 98

Multiple Choice

Write the partial fraction decomposition of the rational expression.
- $\frac { 6 x ^ { 3 } + 4 x ^ { 2 } + 13 x + 15 } { \left( x ^ { 2 } + 3 \right) ^ { 3 } }$

• A) \(\frac { x } { x ^ { 2 } + 3 } + \frac { 6 x + 4 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } } + \frac { - 5 x + 3 } { \left( x ^ { 2 } + 3 \right) ^ { 3 } }\)
• B) \(\frac { x + 1 } { x ^ { 2 } + 3 } + \frac { 6 x + 4 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } } + \frac { - 5 x + 3 } { \left( x ^ { 2 } + 3 \right) ^ { 3 } }\)
• C) \(\frac { 6 x - 4 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } } + \frac { - 5 x - 3 } { \left( x ^ { 2 } + 3 \right) ^ { 3 } }\)
• D) \(\frac { 6 x + 4 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } } + \frac { - 5 x + 3 } { \left( x ^ { 2 } + 3 \right) ^ { 3 } }\)

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