Simplify the Expression $\frac{(1)\left(x^{2}-8\right)^{1 / 2}-x\left[\frac{1}{3}\right]\left(x^{2}-8\right)^{-1 / 2}(3 x)}{\left[\left(x^{2}-8\right)^{1 / 2}\right]^{2}}$

question 145

Multiple Choice

Simplify the expression. Do not rationalize the denominator.
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$\frac{(1) \left(x^{2}-8\right) ^{1 / 2}-x\left[\frac{1}{3}\right]\left(x^{2}-8\right) ^{-1 / 2}(3 x) }{\left[\left(x^{2}-8\right) ^{1 / 2}\right]^{2}}$

• A) \(\frac { 1 - x ^ { 2 } } { \left( x ^ { 2 } - 8 \right) ^ { 5 / 2 } }\)
• B) \(\frac { 1 - x ^ { 2 } } { \left( x ^ { 2 } - 8 \right) ^ { 3 / 2 } }\)
• C) \(- \frac { 8 } { \left( x ^ { 2 } - 8 \right) ^ { 5 / 2 } }\)
• D) \(- \frac { 8 } { \left( x ^ { 2 } - 8 \right) ^ { 3 / 2 } }\)

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Definitions:

Gross Margin

The difference between revenue and cost of goods sold divided by revenue, expressed as a percentage; it measures the profitability of selling goods.

Cost Method

An accounting method used to value investments, where the investment is recorded at cost and adjustments are made for dividends received or additional investments made.

Significant Influence

The power to participate in the financial and operating policy decisions of an investee but not control those policies.

Cost Method

An accounting method used to value an investment, based on the cost to acquire the asset, without recognizing post-purchase market changes.