Write the Partial Fraction Decomposition of the Rational Expression $$\frac { x - 7 } { ( x - 2 ) ( x - 3 ) }$$

question 169

Multiple Choice

Write the partial fraction decomposition of the rational expression.
- $$\frac { x - 7 } { ( x - 2 ) ( x - 3 ) }$$

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

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Definitions:

Prime Costs

The direct costs of manufacturing a product, which include raw material and labor expenses directly tied to the production process.

Conversion Costs

These are costs incurred during the manufacturing process to convert raw materials into finished products, including direct labor and factory overhead expenses.

Depreciation Expense

The allocation of the cost of a tangible asset over its useful life.

Factory Overhead

Costs associated with operating a factory that are not directly tied to a specific product, including maintenance, utilities, and salaries of supervisors.