Write the Form of the Partial Fraction Decomposition of the Rational

question 290

Multiple Choice

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 5 x - 4 } { x ^ { 3 } + 5 x }$

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

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Definitions:

Utility-maximizing Combination

This refers to a situation where a consumer selects a combination of goods and services that provides the highest level of satisfaction or utility, given their budget constraint.

Marginal Utilities

The increased contentment or value obtained by a consumer through the consumption of one extra unit of a good or service.

Diminishing Marginal Utility

The principle that as a person increases consumption of a product, there is a decline in the marginal utility that person derives from consuming each additional unit of that product.

Income Effect

The change in an individual's or economy's income and how that change will affect the quantity demanded of a good or service.