Simplify the Complex Fraction A) $\frac { ( x - 9 ) ( x + 5 ) } { x - 8 } , x \neq - 9 , x \neq 5$

question 140

Multiple Choice

Simplify the complex fraction. $\frac { \left( \frac { x ^ { 2 } - 14 x + 45 } { x ^ { 2 } - 10 x + 25 } \right) } { \left( \frac { 16 + 6 x - x ^ { 2 } } { x ^ { 2 } - 3 x - 40 } \right) }$

• A) \(\frac { ( x - 9 ) ( x + 5 ) } { x - 8 } , x \neq - 9 , x \neq 5\)
• B) \(\frac { ( 5 - x ) ( x + 2 ) } { ( x - 8 ) ( x + 9 ) } , x \neq - 2 , x \neq 9\)
• C) \(\frac { x + 8 } { x - 5 } , x \neq - 8 , x \neq 2\)
• D) \(\frac { x - 9 } { x + 2 } , x \neq 5 , x \neq 9\)
• E) \(\frac { ( 9 - x ) ( x + 5 ) } { ( x - 5 ) ( x + 2 ) } , x \neq - 5 , x \neq 8\)

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Definitions:

Aldehydes

Organic compounds characterized by a carbonyl group bonded to at least one hydrogen atom, making them highly reactive.

Carboxylic Acid Derivative

Compounds obtained by substituting the hydroxyl group in carboxylic acids with other functional groups like halides, amides, or esters.

β-Hydroxybutyronitrile

An organic compound featuring a hydroxyl group (–OH) and a nitrile group (–CN) on a four-carbon chain, positioned beta (β) to each other.

Boiling Point

The temperature at which the vapor pressure of a liquid equals the external pressure surrounding the liquid, causing it to turn into vapor.