Find the Partial Fraction Decomposition for the Rational Expression $$\frac { 8 x - 32 } { ( x + 5 ) ( x - 3 ) }$$

question 474

Multiple Choice

Find the partial fraction decomposition for the rational expression.
- $$\frac { 8 x - 32 } { ( x + 5 ) ( x - 3 ) }$$

• A) \(\frac { 1 } { x - 3 } + \frac { - 9 } { x + 5 }\)
• B) \(\frac { 9 } { x + 5 } + \frac { 1 } { x - 3 }\)
• C) \(\frac { 9 } { x + 5 } + \frac { - 1 } { x - 3 }\)
• D) \(\frac { 8 } { x + 5 } + \frac { - 32 } { x - 3 }\)

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Definitions:

Contribution Margin Ratio

The percentage of each sales dollar that remains after variable costs are subtracted, contributing to covering fixed costs and generating profit.

Fixed Expenses

Costs that do not fluctuate with changes in production level or sales volume, such as rent, insurance, and property taxes.

Cost Structure

The composition of a company's fixed and variable costs, which influences its profitability and pricing strategies.

Special Order

A one-time or unusual order for products or services, often requiring customization or a departure from standard production processes.