Find the Partial Fraction Decomposition for the Rational Expression $$\frac { 3 x ^ { 4 } - 3 x ^ { 3 } + 5 x ^ { 2 } + 12 x + 13 } { ( x + 2 ) ( x - 1 ) ^ { 4 } }$$

question 9

Multiple Choice

Find the partial fraction decomposition for the rational expression.
- $$\frac { 3 x ^ { 4 } - 3 x ^ { 3 } + 5 x ^ { 2 } + 12 x + 13 } { ( x + 2 ) ( x - 1 ) ^ { 4 } }$$

• A) \(\frac { 3 } { x + 2 } + \frac { 1 } { x - 1 } + \frac { 6 } { ( x - 1 ) ^ { 2 } } + \frac { 2 } { ( x - 1 ) ^ { 3 } } + \frac { 1 } { ( x - 1 ) ^ { 4 } }\)
• B) \(\frac { - 1 } { x + 2 } + \frac { 5 } { x - 1 } + \frac { 2 } { ( x - 1 ) ^ { 2 } } + \frac { 17 } { ( x - 1 ) ^ { 3 } } + \frac { 12 } { ( x - 1 ) ^ { 4 } }\)
• C) \(\frac { 5 } { x + 2 } + \frac { 7 } { x - 1 } + \frac { - 2 } { ( x - 1 ) ^ { 2 } } + \frac { 4 } { ( x - 1 ) ^ { 3 } } + \frac { 3 } { ( x - 1 ) ^ { 4 } }\)
• D) \(\frac { 1 } { x + 2 } + \frac { 2 } { x - 1 } + \frac { 3 } { ( x - 1 ) ^ { 2 } } + \frac { 5 } { ( x - 1 ) ^ { 3 } } + \frac { 10 } { ( x - 1 ) ^ { 4 } }\)

Understand the role of money as a medium of exchange and its impact on the economy.

Analyze movements along and shifts of the money demand curve in response to economic variables.

Explain the implications of changes in money supply and demand for the interest rate and overall economic activities.

Understand the pros and cons of using project financing for capital investments.

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Definitions:

Profit Maximization

A process or strategy in which a firm's primary objective is to achieve the highest possible profits by adjusting its production and pricing techniques.

Input Increases

A situation where there is an enhancement or augmentation in the resources used for production.

Marginal Product

The marginal product is the additional output resulting from a one-unit increase in the use of a variable input while holding other inputs constant.

Wage Rate

The amount of compensation that workers receive in exchange for their labor per unit of time.