Find the Partial Fraction Decomposition for the Rational Expression $$\frac { - 2 x ^ { 2 } + 7 x + 24 } { ( x + 3 ) ^ { 2 } ( 3 x + 4 ) }$$

question 163

Multiple Choice

Find the partial fraction decomposition for the rational expression.
- $$\frac { - 2 x ^ { 2 } + 7 x + 24 } { ( x + 3 ) ^ { 2 } ( 3 x + 4 ) }$$

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

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Definitions:

Negatively Correlated

A relationship between two variables in which one variable increases as the other decreases.

Positively Correlated

A term describing two variables that move in the same direction, such that when one variable increases, the other also increases.

Securities' Returns

The profit or loss generated on a security over a particular period, usually expressed as a percentage.

Variances

The quantitative measure of the difference between actual and expected behavior, often used in finance to assess volatility of returns or tracking errors.