Decompose P/Q, Where Q Has a Prime, Repeated Quadratic Factor $$\frac { 5 x ^ { 3 } + 30 x - 6 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$$

question 53

Multiple Choice

Decompose P/Q, Where Q Has a Prime, Repeated Quadratic Factor
Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the
constants.
- $$\frac { 5 x ^ { 3 } + 30 x - 6 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$$

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

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