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:

Compound Proposition

A statement formed by combining two or more propositions using logical connectors (like and, or, not), resulting in a proposition with a more complex structure.

Complete Propositions

Statements or assertions that convey a complete idea, capable of being true or false, and usually containing both a subject and a predicate.

Inclusive Sense

Refers to an understanding or interpretation that aims to encompass or include all relevant aspects or elements.

Disjunction

A compound proposition containing two or more component propositions (the disjuncts) and asserting that at least one of them is true.