Find the Partial Fraction Decomposition for the Rational Expression $\frac { - 3 x ^ { 2 } - 5 x - 42 } { ( x - 3 ) \left( x ^ { 2 } + 3 \right) }$

question 351

Multiple Choice

Find the partial fraction decomposition for the rational expression.
$\frac { - 3 x ^ { 2 } - 5 x - 42 } { ( x - 3 ) \left( x ^ { 2 } + 3 \right) }$

• A) \(\frac { 4 x + 7 } { x ^ { 2 } + 3 } + \frac { - 7 } { x - 3 }\)
• B) \(\frac { 7 x + 4 } { x ^ { 2 } + 3 } + \frac { - 7 } { x - 3 }\)
• C) \(\frac { 4 x + 8 } { x ^ { 2 } + 3 } + \frac { - 7 } { x - 3 }\)
• D) \(\frac { 4 x + 7 } { x ^ { 2 } + 3 } + \frac { 7 } { x - 3 }\)

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Definitions:

Cost of Capital

The rate of return a company must earn on its investments to maintain its market value and attract funds.

Use of Leverage

The practice of using borrowed money to increase the potential return of an investment, which also increases the risk of loss.

Diluting Existing Shares

A process where a company issues more shares, leading to a reduction in the ownership percentage of existing shareholders.

Public Utility

A company providing essential services such as water, electricity, and telecommunications to the public, often subject to government regulation.