Perform the indicated operations.
-$$\frac { x } { x ^ { 2 } - 16 } - \frac { 8 } { x ^ { 2 } + 5 x + 4 }$$
A) $\frac { x ^ { 2 } - 7 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$

B) $\frac { x ^ { 2 } - 7 x + 32 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$

C) $\frac { x ^ { 2 } + 7 x + 32 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$

D) $\frac { x ^ { 2 } - 7 x + 32 } { ( x - 4 ) ( x + 4 ) }$

Question

Perform the indicated operations.
-$$\frac { x } { x ^ { 2 } - 16 } - \frac { 8 } { x ^ { 2 } + 5 x + 4 }$$
A) $\frac { x ^ { 2 } - 7 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$

B) $\frac { x ^ { 2 } - 7 x + 32 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$

C) $\frac { x ^ { 2 } + 7 x + 32 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$

D) $\frac { x ^ { 2 } - 7 x + 32 } { ( x - 4 ) ( x + 4 ) }$

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 $(x - 4)(x + 4)(x + 1)$. Adjust the numerators accordingly and subtract to get $\frac{x^2 - 7x + 32}{(x - 4)(x + 4)(x + 1)}$.

Perform the Indicated Operations xx2−16−8x2+5x+4\frac { x } { x ^ { 2 } - 16 } - \frac { 8 } { x ^ { 2 } + 5 x + 4 }x2−16x​−x2+5x+48​

Perform the Indicated Operations $\frac { x } { x ^ { 2 } - 16 } - \frac { 8 } { x ^ { 2 } + 5 x + 4 }$