Perform the indicated operation. Simplify if possible.
-$\frac { x } { x ^ { 2 } - 16 } - \frac { 5 } { x ^ { 2 } + 5 x + 4 }$
A) $\frac { x ^ { 2 } - 4 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$
B) $\frac { x ^ { 2 } - 4 x + 20 } { ( x - 4 ) ( x + 4 ) }$
C) $\frac { x ^ { 2 } - 4 x + 20 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$
D) $\frac { x ^ { 2 } + 4 x + 20 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$

Question

Quizplus · Accepted Answer

First, factor the denominators: $x^2 - 16$ factors into $(x - 4)(x + 4)$ and $x^2 + 5x + 4$ factors into $(x + 4)(x + 1)$. The least common denominator (LCD) is $(x - 4)(x + 4)(x + 1)$. After finding a common denominator and combining the fractions, the numerator simplifies to $x^2 - 4x + 20$, making the correct answer $\frac{x^2 - 4x + 20}{(x - 4)(x + 4)(x + 1)}$.

Perform the Indicated Operation xx2−16−5x2+5x+4\frac { x } { x ^ { 2 } - 16 } - \frac { 5 } { x ^ { 2 } + 5 x + 4 }x2−16x​−x2+5x+45​

Perform the Indicated Operation $\frac { x } { x ^ { 2 } - 16 } - \frac { 5 } { x ^ { 2 } + 5 x + 4 }$