Write the Partial Fraction Decomposition of the Rational Expression $$\frac { - 4 x ^ { 2 } - 13 x - 12 } { ( x + 2 ) ( x + 1 ) ^ { 2 } }$$

question 163

Multiple Choice

Write the partial fraction decomposition of the rational expression.
- $$\frac { - 4 x ^ { 2 } - 13 x - 12 } { ( x + 2 ) ( x + 1 ) ^ { 2 } }$$

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

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Definitions:

Uncompacted Clay

Clay in its natural, undisturbed state, not subjected to pressure, and therefore retaining its original volume and porosity.

Permeability

The capacity of a rock or soil to transmit water or other fluids through its pore spaces and fractures.

Highly Fractured Granite

Granite rock that has undergone extensive cracking and breaking, often increasing its permeability and affecting its structural integrity.

Insoluble Material

Substances that cannot dissolve in a solvent, such as water, remaining solid and separated from the liquid mixture.