Perform the Operations and Simplify $\frac { 3 u ^ { 2 } + 17 u - 28 } { u ^ { 6 } } \div \frac { 3 u ^ { 2 } + 12 u + 4 } { u ^ { 8 } - 4 u ^ { 7 } }$

question 50

Multiple Choice

Perform the operations and simplify. $\frac { 3 u ^ { 2 } + 17 u - 28 } { u ^ { 6 } } \div \frac { 3 u ^ { 2 } + 12 u + 4 } { u ^ { 8 } - 4 u ^ { 7 } }$

• A) \(\frac { u + 7 } { u ^ { 2 } } , u \neq 0 , u \neq \frac { 4 } { 3 } , u \neq 4\)
• B) \(\frac { u - 4 } { u } , u \neq 0\)
• C) \(\frac { ( u - 4 ) ( u + 7 ) } { u ( u + 1 ) } , u \neq 0\)
• D) \(\frac { ( 3 u - 4 ) ( u - 4 ) } { u ^ { 2 } ( u + 1 ) } , u \neq - 7 , u \neq 0\)
• E) \(\frac { u ( 3 u - 4 ) ( u + 7 ) ( u - 4 ) } { 3 u ^ { 2 } + 12 u + 4 } , u \neq 0 , u \neq 4\)

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Definitions:

Contribution Margin

The amount remaining from sales revenue after variable production costs and variable expenses have been deducted; used to cover fixed costs and to generate profit.

Traceable Fixed Expenses

Fixed costs that can be directly linked to a specific business segment, product, or operation and would disappear if the segment was discontinued.

Common Fixed Expenses

Fixed costs that are not directly attributable to a specific product or service line and must be paid regardless of the level of production or sales.

Contribution Margin

The amount remaining from sales revenue after variable costs have been deducted, indicating how much revenue contributes to covering fixed costs.