Find the Partial Fraction Decomposition for the Rational Expression $$\frac { 4 x ^ { 3 } + 8 x ^ { 2 } - 6 x + 2 } { 2 x ^ { 2 } - x - 1 }$$

question 232

Multiple Choice

Find the partial fraction decomposition for the rational expression.
- $$\frac { 4 x ^ { 3 } + 8 x ^ { 2 } - 6 x + 2 } { 2 x ^ { 2 } - x - 1 }$$

• A) \(2 x + 5 + \frac { - 7 } { 6 x + 3 } + \frac { 13 } { 3 x - 3 }\)
• B) \(2 x + 5 + \frac { - 13 } { 6 x + 3 } + \frac { 8 } { 3 x - 3 }\)
• C) \(2 x - 5 + \frac { - 13 } { 2 x + 1 } + \frac { 7 } { x - 1 }\)
• D) \(2 x - 5 + \frac { - 5 } { 6 x + 3 } + \frac { 1 } { 3 x - 3 }\)

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Definitions:

X-ray Crystallography

A scientific method used to determine the atomic and molecular structure of a crystal by diffracting X-rays through the crystal.

Franklin

Refers to Benjamin Franklin, a prominent American polymath known for his contributions to the founding of the United States and his discoveries and theories regarding electricity.

Wilkins

Maurice Wilkins, a biophysicist who contributed to the discovery of the structure of DNA.

Watson

Watson refers to James Watson, an American molecular biologist, geneticist, and zoologist, best known as one of the co-discoverers of the structure of DNA in 1953 alongside Francis Crick.