Write the Partial Fraction Decomposition of the Rational Expression $$\frac { 8 x + 1 } { ( x - 1 ) \left( x ^ { 2 } + x + 1 \right) }$$

question 286

Multiple Choice

Write the partial fraction decomposition of the rational expression.
- $$\frac { 8 x + 1 } { ( x - 1 ) \left( x ^ { 2 } + x + 1 \right) }$$

• A) \(\frac { 3 } { x - 1 } + \frac { - 3 x + 2 } { x ^ { 2 } + x + 1 }\)
• B) \(\frac { 3 } { x - 1 } + \frac { - 3 } { x + 1 } + \frac { 2 } { x - 1 }\)
• C) \(\frac { - 3 } { x - 1 } + \frac { 3 x + 2 } { x ^ { 2 } + x + 1 }\)
• D) \(\frac { 3 } { x - 1 } + \frac { 2 x - 3 } { x ^ { 2 } + x + 1 }\)

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Definitions:

Retention Ratio

The proportion of a company's net income that is retained rather than paid out as dividends, indicating reinvestment back into the company.

Return on Assets

A financial ratio that indicates how profitable a company is relative to its total assets.

Internal Growth Rate

The maximum rate at which a company can expand using only internal financing without resorting to borrowing or selling equity.

Dividend Payout Ratio

The fraction of earnings a company pays out to its shareholders as dividends, represented as a percentage of its net income.