Subtract.
-$$\frac { x } { x ^ { 2 } - 16 } - \frac { 6 } { x ^ { 2 } + 5 x + 4 }$$
A) $\frac { x ^ { 2 } - 5 x + 24 } { ( x - 4 ) ( x + 4 ) }$

B) $\frac { x ^ { 2 } - 5 x + 24 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$

C) $\frac { x ^ { 2 } - 5 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$

D) $\frac { x ^ { 2 } + 5 x + 24 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$

Question

Subtract.
-$$\frac { x } { x ^ { 2 } - 16 } - \frac { 6 } { x ^ { 2 } + 5 x + 4 }$$
A) $\frac { x ^ { 2 } - 5 x + 24 } { ( x - 4 ) ( x + 4 ) }$

B) $\frac { x ^ { 2 } - 5 x + 24 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$

C) $\frac { x ^ { 2 } - 5 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$

D) $\frac { x ^ { 2 } + 5 x + 24 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$

Quizplus · Accepted Answer

To subtract the fractions, we need a common denominator. Factoring each denominator, we get
$$\frac{x}{x^2-16} - \frac{6}{x^2+5x+4} = \frac{x}{(x-4)(x+4)} - \frac{6}{(x+4)(x+1)}$$
The common denominator is now $(x-4)(x+4)(x+1)$. Multiplying the first fraction by $\frac{x+1}{x+1}$ and the second fraction by $\frac{x-4}{x-4}$, we get
$$\frac{x(x+1)}{(x-4)(x+4)(x+1)} - \frac{6(x-4)}{(x-4)(x+4)(x+1)} = \frac{x^2 + x - 6x + 24}{(x-4)(x+4)(x+1)} = \frac{x^2 - 5x + 24}{(x-4)(x+4)(x+1)}$$
Therefore, the answer is choice B.

Subtract - xx2−16−6x2+5x+4\frac { x } { x ^ { 2 } - 16 } - \frac { 6 } { x ^ { 2 } + 5 x + 4 }x2−16x​−x2+5x+46​

Subtract
- $\frac { x } { x ^ { 2 } - 16 } - \frac { 6 } { x ^ { 2 } + 5 x + 4 }$