Write the Partial Fraction Decomposition of the Improper Rational Expression $\frac { x ^ { 2 } + 4 x } { x ^ { 2 } + x + 1 }$

question 2

Multiple Choice

Write the partial fraction decomposition of the improper rational expression. $\frac { x ^ { 2 } + 4 x } { x ^ { 2 } + x + 1 }$

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

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Definitions:

Call Option

A financial contract that gives the buyer the right, but not the obligation, to buy a stock, bond, commodity, or other asset at a specified price within a specific time period.

Expiration

The date on which a derivative contract such as an option or futures contract becomes void and the right to exercise it no longer exists.

Arbitrage Opportunity

A situation where a trader can profit from differences in price of the same asset in different markets without taking on any risk.

American Put Option

A type of put option that can be exercised at any time before its expiration, allowing the holder to sell the underlying asset at a specified price.