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:

Major Organic Product

The primary product of a chemical reaction that has the highest yield, relative to other potential products.

Cycloheptene

A cyclic hydrocarbon with the molecular formula C7H12, featuring a seven-membered ring with one double bond.

N-Bromosuccinimide

A chemical reagent represented by the formula C4H4BrNO2, often used as a brominating and oxidation agent in organic synthesis.

HOMO

Highest Occupied Molecular Orbital, which is the highest energy molecular orbital that contains electrons in a molecule.