Write the Partial Fraction Decomposition of the Rational Expression $\frac { 5 } { x ^ { 2 } - 5 x }$

question 95

Multiple Choice

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 5 } { x ^ { 2 } - 5 x }$

• A) \(\frac { A } { x } + \frac { B } { x - 5 }\)
• B) \(\frac { 1 } { x + 5 } + \frac { 1 } { x }\)
• C) \(\frac { 1 } { x } - \frac { 1 } { x + 5 }\)
• D) \(\frac { 1 } { x - 5 } - \frac { 1 } { x }\)
• E) \(\frac { A } { x } - \frac { B } { x - 5 }\)

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Definitions:

Marginal Social Cost

The total cost to society of producing an additional unit of a good or service, taking into account the cost to producers and any costs to other members of society.

Sulfur Emissions

The release of sulfur compounds, primarily sulfur dioxide (SO2), into the atmosphere, often from industrial processes, causing environmental pollution and acid rain.

MSB > MSC

A condition where the marginal social benefit of consuming a good or service exceeds the marginal social cost, often justifying governmental intervention.

Methane Gas

A colorless, odorless gas that is a significant component of natural gas.