Write the Partial Fraction Decomposition of the Rational Expression $\frac { x ^ { 2 } - 111 } { x ^ { 4 } - x ^ { 2 } - 72 }$

question 124

Multiple Choice

Write the partial fraction decomposition of the rational expression.
- $\frac { x ^ { 2 } - 111 } { x ^ { 4 } - x ^ { 2 } - 72 }$

• A) \(\frac { 1 } { x + 3 } - \frac { 1 } { x - 3 } + \frac { 7 } { x ^ { 2 } + 8 }\)
• B) \(\frac { 1 } { x + 3 } + \frac { 1 } { x - 3 } + \frac { 7 } { x ^ { 2 } + 8 }\)
• C) \(\frac { 1 } { x + 3 } + \frac { 1 } { x - 3 } - \frac { 7 } { x ^ { 2 } + 8 }\)
• D) \(\frac { 1 } { x + 3 } - \frac { 1 } { x - 3 } - \frac { 7 } { x ^ { 2 } + 8 }\)

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Definitions:

Independent Trials

Experiments or trials in which the outcome of one trial does not affect the outcome of any other trials.

Binomial Experiment

A statistical experiment that has two possible outcomes for each trial and a fixed number of trials, where each trial is independent of the others.

Probability

A numerical expression of an event's probability, with the scale going from 0, symbolizing that the event cannot occur, to 1, signifying guaranteed occurrence.

Probability of Failure

The likelihood or chance that a system or component will fail to perform its required function within a specified period under normal operating conditions.