Question #N369
The expression $\frac{x^2 - 2x - 8}{x^2 - 16}$ is equivalent to which of the following expressions, where $x \neq 4$ and $x \neq -4$?
A. $\frac{x-4}{x-2}$
B. $\frac{x + 2}{x + 4}$
C. $\frac{x-2}{x+4}$
D. $\frac{x + 4}{x - 2}$
Correct Answer is: C
We can factor the numerator and denominator of the given expression: $\frac{x^2 - 2x - 8}{x^2 - 16} = \frac{(x-4)(x+2)}{(x+4)(x-4)}$ Since $x \neq 4$ and $x \neq -4$, we can cancel the common factors, leaving us with $\frac{x-2}{x+4}$.