Add or subtract as indicated. Write the answer in lowest terms.
-$\frac{x}{x^{2}-16}-\frac{7}{x^{2}+5 x+4}$

A) $\frac{x^{2}+6 x+28}{(x-4)(x+4)(x+1)}$

B) $\frac{x^{2}-6 x+28}{(x-4)(x+4)(x+1)}$

C) $\frac{x^{2}-6 x+28}{(x-4)(x+4)}$

D) $\frac{x^{2}-6}{(x-4)(x+4)(x+1)}$

Question

Add or subtract as indicated. Write the answer in lowest terms.
-$\frac{x}{x^{2}-16}-\frac{7}{x^{2}+5 x+4}$

A) $\frac{x^{2}+6 x+28}{(x-4)(x+4)(x+1)}$

B) $\frac{x^{2}-6 x+28}{(x-4)(x+4)(x+1)}$

C) $\frac{x^{2}-6 x+28}{(x-4)(x+4)}$

D) $\frac{x^{2}-6}{(x-4)(x+4)(x+1)}$

Quizplus · Accepted Answer

First, factor the denominators: $x^2 - 16 = (x-4)(x+4)$ and $x^2 + 5x + 4 = (x+4)(x+1)$. To subtract the fractions, find a common denominator, which is $(x-4)(x+4)(x+1)$. Adjust the numerators accordingly and subtract, simplifying to $\frac{x^2 - 6x + 28}{(x-4)(x+4)(x+1)}$.