Find the Partial Fraction Decomposition for the Rational Expression $$\frac { - 4 x ^ { 2 } - 2 x - 42 } { ( x - 3 ) \left( x ^ { 2 } + 3 \right) }$$

question 506

Multiple Choice

Find the partial fraction decomposition for the rational expression.
- $$\frac { - 4 x ^ { 2 } - 2 x - 42 } { ( x - 3 ) \left( x ^ { 2 } + 3 \right) }$$

• A) \(\frac { 3 x + 7 } { x ^ { 2 } + 3 } + \frac { 7 } { x - 3 }\)
• B) \(\frac { 7 x + 3 } { x ^ { 2 } + 3 } + \frac { - 7 } { x - 3 }\)
• C) \(\frac { 3 x + 8 } { x ^ { 2 } + 3 } + \frac { - 7 } { x - 3 }\)
• D) \(\frac { 3 x + 7 } { x ^ { 2 } + 3 } + \frac { - 7 } { x - 3 }\)

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Definitions:

Consumption Choice

This refers to the selection of a combination of goods and services that individuals or households decide to consume based on their preferences, income, and prices.

Budget Constraint

A limit on the consumption possibilities of an individual or entity based on available resources.

Optimal Consumption

Describes the combination of goods and services that maximizes an individual's utility or satisfaction subject to their budget constraint.

Marginal Utility

The additional satisfaction or benefit gained from consuming or using one more unit of a good or service.