Find the Partial Fraction Decomposition for the Rational Expression $$\frac { - 2 x ^ { 2 } + 3 x + 8 } { ( x + 1 ) ^ { 2 } ( 3 x + 4 ) }$$

question 3

Multiple Choice

Find the partial fraction decomposition for the rational expression.
- $$\frac { - 2 x ^ { 2 } + 3 x + 8 } { ( x + 1 ) ^ { 2 } ( 3 x + 4 ) }$$

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

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Definitions:

Independent Events

Two or more events whose outcomes do not affect each other, meaning the occurrence of one event does not change the probability of the other.

Probability

A measure of the likelihood that an event will occur, expressed as a number between 0 and 1, where 1 indicates certainty.

Marginal Probability

The probability of an event occurring, irrespective of the outcomes of other variables.

P(A or B)

The probability that at least one of two events A or B occurs.