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

question 218

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

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Definitions:

Normal Distribution

A statistical distribution where data points form a symmetric, bell-shaped curve around the mean, indicating that values near the mean are more frequent in occurrence than those far from the mean.

Standard Deviation

A statistic that measures the dispersion of a dataset relative to its mean, indicating how spread out the values in the dataset are.

Variance of Returns

A measure used to quantify the volatility of returns from an investment, indicating the dispersion of returns around the mean.

Squared Deviations

The squared differences between each data point in a set and the set's mean, used in statistical analysis to measure variance.