Add or subtract.
-$\frac { x } { x ^ { 2 } - 16 } - \frac { 3 } { x ^ { 2 } + 5 x + 4 }$
A) $\frac { x ^ { 2 } + 2 x + 12 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$
B) $\frac { x ^ { 2 } - 2 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$
C) $\frac { x ^ { 2 } - 2 x + 12 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$
D) $\frac { x ^ { 2 } - 2 x + 12 } { ( x - 4 ) ( x + 4 ) }$

Question

Quizplus · Accepted Answer

To solve this, first factor the denominators: $x^2 - 16 = (x - 4)(x + 4)$ and $x^2 + 5x + 4 = (x + 4)(x + 1)$. The common denominator is $(x - 4)(x + 4)(x + 1)$. Adjusting the numerators to have a common denominator gives: $\frac{x(x + 1) - 3(x - 4)}{(x - 4)(x + 4)(x + 1)}$, simplifying to $\frac{x^2 - 2x + 12}{(x - 4)(x + 4)(x + 1)}$.

Add or Subtract xx2−16−3x2+5x+4\frac { x } { x ^ { 2 } - 16 } - \frac { 3 } { x ^ { 2 } + 5 x + 4 }x2−16x​−x2+5x+43​

Add or Subtract $\frac { x } { x ^ { 2 } - 16 } - \frac { 3 } { x ^ { 2 } + 5 x + 4 }$