Find the Partial Fraction Decomposition for the Rational Expression $$\frac { 2 x ^ { 3 } - 7 x ^ { 2 } + 5 x - 3 } { x ^ { 2 } + x - 2 }$$

question 69

Multiple Choice

Find the partial fraction decomposition for the rational expression.
- $$\frac { 2 x ^ { 3 } - 7 x ^ { 2 } + 5 x - 3 } { x ^ { 2 } + x - 2 }$$

• A) \(2 x - 9 + \frac { - 5 / 3 } { x + 2 } + \frac { 1 / 3 } { x - 1 }\)
• B) \(2 x - 9 + \frac { 19 } { x + 2 } - \frac { - 1 } { x - 1 }\)
• C) \(2 x + 5 + \frac { - 7 / 3 } { x + 2 } + \frac { 13 / 3 } { x - 1 }\)
• D) \(2 x + 9 + \frac { - 13 } { x + 2 } + \frac { 7 } { x - 1 }\)

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Definitions:

Short-Run Equilibrium

A state in a market where supply equals demand, but only considering a period in which some factors, like production capacity, remain constant.

Constant-Cost Industry

An industry in which the entry and exit of firms have no effect on the prices firms in the industry must pay for resources and thus no effect on production costs.

Long-Run Economic Profits

Profits earned by a firm when all resources are adjusted to their long-term optimal level, indicating the firm is in equilibrium and cannot earn higher profits by altering production.

Free Entry And Exit

A situation in a market where firms can enter and leave the industry without facing significant barriers or costs, promoting competition.