Which Fraction Appears in the Partial Fraction Decomposition Of $\frac { 5 x ^ { 2 } + 17 x + 12 } { x ( x + 2 ) ^ { 2 } }$

question 18

Multiple Choice

Which fraction appears in the partial fraction decomposition of $\frac { 5 x ^ { 2 } + 17 x + 12 } { x ( x + 2 ) ^ { 2 } }$ ?

• A) \(\frac { 1 } { ( x + 2 ) ^ { 2 } }\)
• B) \(\frac { 2 } { x }\)
• C) \(\frac { 5 } { x }\)
• D) \(\frac { 3 } { ( x + 2 ) ^ { 2 } }\)
• E) \(\frac { 1 } { x + 2 }\)

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Definitions:

AVC

Average Variable Cost, which is the total variable costs of production divided by the quantity of output produced.

MC

MC, or Marginal Cost, is the cost of producing one additional unit of a product, crucial for understanding profit maximization in businesses.

Marginal Revenue

The additional income from selling one more unit of a good; essentially the change in total revenue from an additional unit sold.

Perfect Competition

An idealized market structure in which there are many buyers and sellers, no barriers to entering or exiting the market, and products are identical.