Simplify the Rational Expression $\frac { 25 \left( x ^ { 2 } - 3 \right) ^ { 3 } + 125 x \left( x ^ { 2 } - 3 \right) ^ { 4 } } { 625 \left( x ^ { 2 } - 3 \right) ^ { 3 } }$

question 363

Multiple Choice

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
- $\frac { 25 \left( x ^ { 2 } - 3 \right) ^ { 3 } + 125 x \left( x ^ { 2 } - 3 \right) ^ { 4 } } { 625 \left( x ^ { 2 } - 3 \right) ^ { 3 } }$

• A) \(\frac { 1 + 5 x ^ { 3 } - 15 x } { 25 }\)
• B) \(\frac { 1 - 5 x ^ { 3 } - 15 x } { 125 }\)
• C) \(\frac { 1 + 5 x ^ { 3 } + 15 x } { 25 }\)
• D) \(\frac { 1 - 5 x ^ { 3 } + 15 x } { 125 }\)

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Increasing Cost Industry

An industry where production costs rise as output increases due to factors such as limited resources or higher wages.

Resource Prices

The cost associated with acquiring resources or inputs, such as labor, raw materials, and capital, used in the production of goods and services.

Long-run Market Supply

Refers to the total amount of goods that can be produced and made available in the market over a long period, considering all resources are variable.

Wheat Farmers

Individuals or entities engaged in the cultivation of wheat as a crop, playing a vital role in global food supply and commodities markets.