Write the Partial Fraction Decomposition of the Rational Expression $\frac { 3 x - 2 } { x ^ { 3 } - 1 }$

question 76

Multiple Choice

Write the partial fraction decomposition of the rational expression.
- $\frac { 3 x - 2 } { x ^ { 3 } - 1 }$

• A) \(\frac { 3 } { x - 1 } + \frac { - 3 ( x - 7 ) } { x ^ { 2 } + x + 1 }\)
• B) \(\frac { \frac { 1 } { 2 } } { x - 1 } + \frac { \frac { 5 } { 2 } } { x + 1 }\)
• C) \(\frac { \frac { 1 } { 3 } } { x - 1 } + \frac { - \frac { 1 } { 3 } x + \frac { 7 } { 3 } } { \left( x ^ { 2 } + x + 1 \right) }\)
• D) \(\frac { 3 } { ( x - 1 ) ^ { 2 } } + \frac { 1 } { ( x - 1 ) ^ { 3 } }\)

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Definitions:

Short-Day Plant

A plant that flowers only when the period of daylight is shorter than a certain critical length, typically in late summer, autumn, or winter.

Cocklebur

Cocklebur refers to plants in the genus Xanthium, characterized by their spiny burrs that adhere to animals and clothing for seed dispersal.

Day-Neutral Plant

A plant whose flowering is not controlled by variations in day length that occur with changing seasons. Compare with long-day, short-day, and intermediate-day plants.

Long-Day Plant

A plant that flowers only after being exposed to light periods longer than a certain critical length, often found in summer.