Subtract. Simplify, if possible.
-$$\frac { x } { x ^ { 2 } - 16 } - \frac { 8 } { x ^ { 2 } + 5 x + 4 }$$
A) $\frac { x ^ { 2 } - 7 x + 32 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$

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

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

Subtract. Simplify, if possible.
-$$\frac { x } { x ^ { 2 } - 16 } - \frac { 8 } { x ^ { 2 } + 5 x + 4 }$$
A) $\frac { x ^ { 2 } - 7 x + 32 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$

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

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

The correct answer is obtained by factoring the denominators and finding a common denominator, then subtracting the numerators accordingly. The first denominator $x^2 - 16$ factors into $(x - 4)(x + 4)$, and the second denominator $x^2 + 5x + 4$ factors into $(x + 4)(x + 1)$. The common denominator is $(x - 4)(x + 4)(x + 1)$. After aligning the fractions to this common denominator and subtracting, the numerator simplifies to $x^2 - 7x + 32$.

Subtract Simplify, If Possible xx2−16−8x2+5x+4\frac { x } { x ^ { 2 } - 16 } - \frac { 8 } { x ^ { 2 } + 5 x + 4 }x2−16x​−x2+5x+48​

Subtract Simplify, If Possible $\frac { x } { x ^ { 2 } - 16 } - \frac { 8 } { x ^ { 2 } + 5 x + 4 }$