Write the Partial Fraction Decomposition of the Rational Expression $\frac { 3 x ^ { 3 } + 3 x ^ { 2 } } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$

question 203

Multiple Choice

Write the partial fraction decomposition of the rational expression.
- $\frac { 3 x ^ { 3 } + 3 x ^ { 2 } } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$

• A) \(\frac { 3 x - 3 } { x ^ { 2 } + 5 } + \frac { - 15 x + 15 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }\)
• B) \(\frac { 3 x + 3 } { x ^ { 2 } + 5 } + \frac { 15 x - 15 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }\)
• C) \(\frac { 3 x + 3 } { x ^ { 2 } + 5 } + \frac { 15 x + 15 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }\)
• D) \(\frac { 3 x + 3 } { x ^ { 2 } + 5 } + \frac { - 15 x - 15 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }\)

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Definitions:

Mutual Interdependence

occurs in markets where the actions of one firm affect the outcomes of other firms, often seen in oligopolistic markets where a few companies dominate.

Homogeneous

Describes products, services, or entities that are uniform in nature, lacking differentiation.

Differentiated

Describes products or services that are distinct from those of competitors in at least one aspect, as perceived by the market.

Pricing Strategy

An approach or plan used by a business to determine the best price for its products or services to maximize profits and meet market demands.