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

question 3

Multiple Choice

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

• A) \(\frac { 4 } { 3 x + 4 } + \frac { 2 } { ( x + 1 ) ^ { 2 } } + \frac { - 3 } { x + 1 }\)
• B) \(\frac { 4 } { 3 x + 4 } + \frac { - 3 } { ( x + 1 ) ^ { 2 } } + \frac { - 2 } { x + 1 }\)
• C) \(\frac { 4 } { 3 x + 4 } + \frac { 3 } { ( x + 1 ) ^ { 2 } } + \frac { 2 } { x + 1 }\)
• D) \(\frac { 4 } { 3 x + 4 } + \frac { - 2 } { x + 1 } + \frac { 3 } { ( x + 1 ) ^ { 2 } }\)

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Definitions:

Worn

Showing signs of use or aging, typically in the context of clothing, goods, or machinery having diminished quality or condition over time.

Marginal Product

The additional output resulting from the use of one more unit of a variable input, while holding other inputs constant.

Variable Cost

Variable cost is the type of cost that varies with the level of output or production, such as materials and labor costs.

Marginal Product

The additional output produced by using one more unit of a input, holding all other inputs constant, used in the analysis of production efficiency.