Write the Form of the Partial Fraction Decomposition of the Rational

question 295

Multiple Choice

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { 6 x ^ { 2 } - 1 } { ( x + 8 ) ^ { 3 } }$

• A) \(\frac { A } { x + 8 } + \frac { B x } { ( x + 8 ) ^ { 2 } } + \frac { C x ^ { 2 } } { ( x + 8 ) ^ { 3 } }\)
• B) \(\frac { A x + B } { x + 8 } + \frac { C x + D } { ( x + 8 ) ^ { 2 } } + \frac { E x + F } { ( x + 8 ) ^ { 3 } }\)
• C) \(\frac { A x ^ { 2 } } { ( x + 8 ) ^ { 3 } } + \frac { B } { ( x + 8 ) ^ { 3 } }\)
• D) \(\frac { A } { x + 8 } + \frac { B } { ( x + 8 ) ^ { 2 } } + \frac { C } { ( x + 8 ) ^ { 3 } }\)
• E) \(\frac { A } { x + 8 } + \frac { B } { ( x + 8 ) ^ { 2 } }\)

---

Definitions:

Asymmetric Information

Asymmetric information occurs when one party in a transaction has more or better information than the other, leading to an imbalance in the decision-making process.

Unsuspecting Buyer

A consumer who purchases goods or services without being aware of all the relevant information, often leading to disadvantageous situations.

Auto Transmission

A type of vehicle transmission that automatically changes gear ratios as the vehicle moves, without input from the driver.

Adverse Selection

A situation in insurance and other markets where buyers and sellers have different information, leading those more likely to produce negative outcomes to participate more actively.