Find the Partial Fraction Decomposition for the Rational Expression $\frac { 2 x ^ { 3 } - 7 x ^ { 2 } + 5 x - 3 } { x ^ { 2 } + x - 2 }$

question 159

Multiple Choice

Find the partial fraction decomposition for the rational expression.
- $\frac { 2 x ^ { 3 } - 7 x ^ { 2 } + 5 x - 3 } { x ^ { 2 } + x - 2 }$

• A) \(2 x + 9 + \frac { - 13 } { x + 2 } + \frac { 7 } { x - 1 }\)
• B) \(2 x + 5 + \frac { - 7 / 3 } { x + 2 } + \frac { 13 / 3 } { x - 1 }\)
• C) \(2 x - 9 + \frac { 19 } { x + 2 } - \frac { - 1 } { x - 1 }\)
• D) \(2 x - 9 + \frac { - 5 / 3 } { x + 2 } + \frac { 1 / 3 } { x - 1 }\)

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Definitions:

Diffusion of Innovation

Diffusion of innovation is the process by which a new idea, product, or behavior is accepted and adopted by the market or a community over time.

Diffusion of Innovation

A theory that describes how, why, and at what rate new ideas and technology spread through cultures and societies, from early adopters to more widespread acceptance.

Diffusion of Innovation

The process by which a new idea, product, or behavior spreads through a population, influencing the adoption rate and market saturation.

Early Adopters

A group within a consumer base that is among the first to acquire and use a new product or technology, often influencing others.