Simplify the Rational Expression $$\frac { 16 \left( x ^ { 2 } - 3 \right) ^ { 3 } + 64 x \left( x ^ { 2 } - 3 \right) ^ { 4 } } { 256 \left( x ^ { 2 } - 3 \right) ^ { 3 } }$$

question 291

Multiple Choice

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
- $$\frac { 16 \left( x ^ { 2 } - 3 \right) ^ { 3 } + 64 x \left( x ^ { 2 } - 3 \right) ^ { 4 } } { 256 \left( x ^ { 2 } - 3 \right) ^ { 3 } }$$

• A) \(\frac { 1 - 4 x ^ { 3 } + 12 x } { 64 }\)
• B) \(\frac { 1 - 4 x ^ { 3 } - 12 x } { 64 }\)
• C) \(\frac { 1 + 4 x ^ { 3 } - 12 x } { 16 }\)
• D) \(\frac { 1 + 4 x ^ { 3 } + 12 x } { 16 }\)

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Definitions:

Heat

A form of energy associated with the movement of atoms and molecules in any material.

Evaporation

Transition of a liquid to a vapor.

Coelomic Fluid

Fluid found within the coelom, the body cavity of most animals, which aids in the transport of gases, nutrients, and waste materials.

Nephridia

Excretory organs in many invertebrates, including annelids, that serve to remove metabolic wastes from an organism’s body.