Write the Partial Fraction Decomposition of the Rational Expression $\frac { 6 x ^ { 3 } + 5 x ^ { 2 } + 32 x + 26 } { \left( x ^ { 2 } + 6 \right) ^ { 3 } }$

question 133

Multiple Choice

Write the partial fraction decomposition of the rational expression.
- $\frac { 6 x ^ { 3 } + 5 x ^ { 2 } + 32 x + 26 } { \left( x ^ { 2 } + 6 \right) ^ { 3 } }$

• A) \(\frac { 6 x - 5 } { \left( x ^ { 2 } + 6 \right) ^ { 2 } } + \frac { - 4 x + 4 } { \left( x ^ { 2 } + 6 \right) ^ { 3 } }\)
• B) \(\frac { 6 x + 5 } { \left( x ^ { 2 } + 6 \right) ^ { 2 } } + \frac { - 4 x - 4 } { \left( x ^ { 2 } + 6 \right) ^ { 3 } }\)
• C) \(\frac { x } { x ^ { 2 } + 6 } + \frac { 6 x + 5 } { \left( x ^ { 2 } + 6 \right) ^ { 2 } } + \frac { - 4 x - 4 } { \left( x ^ { 2 } + 6 \right) ^ { 3 } }\)
• D) \(\frac { x + 1 } { x ^ { 2 } + 6 } + \frac { 6 x + 5 } { \left( x ^ { 2 } + 6 \right) ^ { 2 } } + \frac { - 4 x - 4 } { \left( x ^ { 2 } + 6 \right) ^ { 3 } }\)

Distinguish between business risk and financial risk and their sources.

Understand the effects of financial leverage on WACC and the firm's cost of equity.

Analyze the impact of debt financing on firm value, considering direct bankruptcy costs and tax shields.

Differentiate between unlevered and levered cost of capital and their implications for firm valuation and investment decisions.

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Definitions:

Fecundity

Describes the reproductive capacity of an individual, such as the number and quality of eggs or sperm. As a measure of relative fitness, fecundity refers to the number of offspring produced by an organism.

Continual Reproduction

The ability of an organism to produce offspring repeatedly over its lifetime.

Mature At Birth

Refers to organisms that are born in an advanced state, with the ability to survive without parental care immediately.

Extrinsic Mortality

Refers to the death rate in a population due to external factors, such as predation, disease, or accidents, rather than aging or intrinsic biological factors.