Write the Partial Fraction Decomposition of the Rational Expression $\frac { - 3 x ^ { 2 } - 3 x + 27 } { x ^ { 2 } ( x + 3 ) }$

question 262

Multiple Choice

Write the partial fraction decomposition of the rational expression. $\frac { - 3 x ^ { 2 } - 3 x + 27 } { x ^ { 2 } ( x + 3 ) }$

• A) \(\frac { 1 } { x + 3 } + \frac { 9 } { x ^ { 2 } }\)
• B) \(\frac { 1 } { x + 3 } - \frac { 4 } { x } + \frac { 2 } { x ^ { 2 } }\)
• C) \(\frac { 1 } { x + 3 } - \frac { 4 } { x } + \frac { 9 } { x ^ { 2 } }\)
• D) \(\frac { 1 } { x + 3 } + \frac { 4 } { x } - \frac { 9 } { x ^ { 2 } }\)
• E) \(\frac { - 3 } { x + 3 } - \frac { 3 } { x ( x + 3 ) } + \frac { 27 } { x ^ { 2 } ( x + 3 ) }\)

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Definitions:

Production Manager

An individual responsible for overseeing the production process, managing production staff, and ensuring that manufacturing processes are efficient and effective.

Variable Overhead Efficiency Variance

The difference between the actual and expected (or standard) variable overhead costs based on the actual production hours.

Standard Activity

A benchmark or norm for measuring performance or efficiency, often used in costing and budgeting processes.

Predetermined Overhead Rate

A rate used to allocate manufacturing overhead to individual products or job orders, calculated before the production period based on estimated costs and activity levels.