Write the Expression with Only Positive Exponents and Evaluate If $$\frac { 1 } { h } \left( \frac { 1 } { ( x + h ) ^ { 2 } + 2 } - \frac { 1 } { x ^ { 2 } + 2 } \right)$$

question 477

Multiple Choice

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
- $$\frac { 1 } { h } \left( \frac { 1 } { ( x + h ) ^ { 2 } + 2 } - \frac { 1 } { x ^ { 2 } + 2 } \right)$$

• A) \(\frac { - 2 x + h } { ( x + h ) ^ { 2 } \left( x ^ { 2 } + 2 \right) }\)
• B) \(\frac { 2 x + h } { \left( ( x + h ) ^ { 2 } + 2 \right) \left( x ^ { 2 } + 2 \right) }\)
• C) \(\frac { 2 x } { \left( ( x + h ) ^ { 2 } + 2 \right) }\)
• D) \(\frac { - 2 x - h } { \left( ( x + h ) ^ { 2 } + 2 \right) \left( x ^ { 2 } + 2 \right) }\)

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Definitions:

Total Product

The total amount of goods or services produced by a firm or an economy at a given level of resource utilization.

Marginal Product

The additional output generated by employing one more unit of a specific factor of production, holding all other factors constant.

Total Product

The total quantity of output or goods produced by a firm or company using a given quantity of inputs during a specific time period.