Question #N408
The expression $\frac{x^2 - 16}{x^2 - 6x + 8}$ is equivalent to $\frac{x + 4}{x - 2}$ when $x \neq 2$ or $x \neq 4$. What is the simplified form of the expression $\frac{x^2 - 16}{x^2 - 6x + 8}$ when $x \neq 2$ or $x \neq 4$?
A. $\frac{x+4}{x-2}$
B. $\frac{x-4}{x-2}$
C. $\frac{x+2}{x-4}$
D. $\frac{x-2}{x+4}$
Correct Answer is: A
We begin by factoring the numerator and denominator: $\frac{x^2 - 16}{x^2 - 6x + 8} = \frac{(x + 4)(x - 4)}{(x - 2)(x - 4)}$. Because $x \neq 2$ or $x \neq 4$, we can cancel out the common factor of $(x - 4)$, leaving us with $\frac{x+4}{x-2}$.