Write the Partial Fraction Decomposition of the Rational Expression $\frac { 3 x ^ { 2 } + 7 x + 7 } { x ^ { 3 } + x }$

question 248

Multiple Choice

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 3 x ^ { 2 } + 7 x + 7 } { x ^ { 3 } + x }$

• A) \(\frac { 7 } { x } - \frac { 4 x + 7 } { x ^ { 2 } + 1 }\)
• B) \(\frac { 7 } { x } + \frac { 4 x - 7 } { x ^ { 2 } + 1 }\)
• C) \(\frac { 7 } { x } + \frac { 4 x + 7 } { x ^ { 2 } + 1 }\)
• D) \(\frac { 7 } { x } - \frac { 7 x - 7 } { x ^ { 2 } + 1 }\)
• E) \(\frac { 7 } { x } - \frac { 4 x - 7 } { x ^ { 2 } + 1 }\)

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Definitions:

Variable Overhead

The overhead costs that fluctuate with the level of production activity, such as utilities and materials used in production.

Product Costs

The costs directly associated with the production of goods, including materials, labor, and manufacturing overhead.

Absorption Costing

A bookkeeping approach encompassing the entirety of production expenses, such as direct materials, direct labor, and both fluctuating and consistent overhead costs, within a product's price.

Production Costs

Expenses associated with the process of producing goods or services.