Find the Partial Fraction Decomposition for the Rational Expression $\frac { 4 x ^ { 3 } + 8 x ^ { 2 } - 6 x + 2 } { 2 x ^ { 2 } - x - 1 }$

question 274

Multiple Choice

Find the partial fraction decomposition for the rational expression.
$\frac { 4 x ^ { 3 } + 8 x ^ { 2 } - 6 x + 2 } { 2 x ^ { 2 } - x - 1 }$

• A) \(2 x - 5 + \frac { - 13 } { 2 x + 1 } + \frac { 7 } { x - 1 }\)
• B) \(2 x - 5 + \frac { - 5 } { 6 x + 3 } + \frac { 1 } { 3 x - 3 }\)
• C) \(2 x + 5 + \frac { - 7 } { 6 x + 3 } + \frac { 13 } { 3 x - 3 }\)
• D) \(2 x + 5 + \frac { - 13 } { 6 x + 3 } + \frac { 8 } { 3 x - 3 }\)

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Definitions:

Blood Pressure

The pressure exerted by circulating blood upon the walls of blood vessels, often measured to assess heart and vascular health.

Tricuspid Valve

A valve in the human heart that lies between the right atrium and the right ventricle, preventing backflow of blood.

Diastole

The stage of the cardiac cycle during which the heart muscle unwinds and the chambers are permitted to be replenished with blood.

Systole

The phase of the heartbeat during which the heart contracts and pumps blood from the chambers into the arteries.