Write the Partial Fraction Decomposition of the Rational Expression $\frac { 7 x ^ { 2 } - 3 x - 6 } { x ^ { 3 } - x }$

question 42

Multiple Choice

Write the partial fraction decomposition of the rational expression.​ $\frac { 7 x ^ { 2 } - 3 x - 6 } { x ^ { 3 } - x }$ ​

• A) \(\frac { 6 } { x } + \frac { 2 } { x - 1 } - \frac { 1 } { x - 1 }\)
• B) \(\frac { 6 } { x } + \frac { 2 } { x + 1 } + \frac { 1 } { x - 1 }\)
• C) \(\frac { 6 } { x } - \frac { 2 } { x + 1 } - \frac { 1 } { x - 1 }\)
• D) \(\frac { 6 } { x } + \frac { 2 } { x + 1 } - \frac { 1 } { x + 1 }\)
• E) \(\frac { 6 } { x } + \frac { 2 } { x + 1 } - \frac { 1 } { x - 1 }\)

---

Definitions:

Attraction

The force that draws particles together, responsible for the interactions between atoms and molecules.

Crystalline Polymers

Polymers with a highly ordered molecular structure, leading to sharp melting points and often high degrees of strength and rigidity.

Thermoplastics

A type of plastic material that becomes moldable above a specific temperature and solidifies upon cooling, allowing for easy reshaping.

Isotactic

Referring to a configuration in polymers where all substituents on the polymer chain are arranged on the same side.