Combine and Simplify $\frac { x } { x ^ { 2 } - 49 } + \frac { 4 } { x ^ { 2 } - 10 x + 21 }$

question 45

Multiple Choice

Combine and simplify. $\frac { x } { x ^ { 2 } - 49 } + \frac { 4 } { x ^ { 2 } - 10 x + 21 }$

• A) \(\frac { x + 4 } { ( x + 7 ) ( x - 7 ) }\)
• B) \(\frac { x ^ { 2 } + x + 4 } { ( x + 7 ) ( x - 7 ) }\)
• C) \(\frac { x ^ { 2 } + x + 28 } { ( x + 7 ) ( x - 7 ) ( x - 3 ) }\)
• D) \(\frac { x ^ { 2 } + 3 x + 12 } { ( x + 7 ) ( x - 7 ) ( x - 3 ) }\)
• E) \(\frac { x ^ { 2 } + 4 x + 21 } { ( x + 7 ) ( x - 7 ) ( x - 3 ) }\)

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Key Feature

A distinctive attribute or aspect that is critical or essential to the understanding or functioning of something.

Potential Scrutiny

The likelihood or possibility of being examined or investigated closely, often in a critical manner.

Ego-Syntonic

Pertaining to thoughts, impulses, and behaviors that are consistent with the self-image of an individual, often seen in conditions like Obsessive Compulsive Disorder.

Ego-Dystonic

Refers to thoughts, impulses, and behaviors that are felt to be repugnant, distressing, unacceptable, and inconsistent with one's self-concept.