Find the Partial Fraction Decomposition for the Given Rational Expression

question 64

Multiple Choice

Find the partial fraction decomposition for the given rational expression. Use the technique of Gaussian
elimination to find A, B, and C.
- $$\frac { - 3 x ^ { 2 } + 7 x - 10 } { ( x + 2 ) ( x - 1 ) ^ { 2 } } = \frac { A } { x + 2 } + \frac { B } { x - 1 } - \frac { C } { ( x - 1 ) ^ { 2 } }$$

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

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Definitions:

Large Lots

Refers to the practice of bulk buying or producing goods in significant quantities to achieve economies of scale.

Fixed Cost

Expenses that do not change with the level of goods or services produced over the short term.

Monthly Demand

The total amount of a product or service that consumers want to purchase over the course of a single month.

Holding Cost

The costs linked to holding inventory that hasn't been sold, such as storage fees, insurance costs, depreciation, and the loss of potential income.