Find the Partial Fraction Decomposition for the Rational Expression $$\frac { - 2 x ^ { 2 } + 7 x + 24 } { ( x + 3 ) ^ { 2 } ( 3 x + 4 ) }$$

question 163

Multiple Choice

Find the partial fraction decomposition for the rational expression.
- $$\frac { - 2 x ^ { 2 } + 7 x + 24 } { ( x + 3 ) ^ { 2 } ( 3 x + 4 ) }$$

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

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Definitions:

Perennial

Describes plants that live for more than two years or streams that flow continuously throughout the year.

Gradient

A rate of inclination or slope, or the rate at which a physical quantity changes with respect to change in another quantity.

Cross-sectional Area

The area of a particular section of an object or material that is exposed when it is cut through by a plane.

Deposition

The geological process by which sediments, soil, and rocks are added to a landform or landmass, often carried by wind, water, or ice.