Decompose P/Q, Where Q Has a Prime, Repeated Quadratic Factor $\frac { x ^ { 2 } + 4 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$

question 283

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.
- $\frac { x ^ { 2 } + 4 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$

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

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Definitions:

Assignable Causes

Specific reasons for variations in a process that can be identified and often corrected, unlike random causes that are inherent to the process.

Natural Causes

Reasons or factors that occur in nature and cause events or conditions without human intervention.