Simplify the rational expression. State any restrictions on the variable. (x^2-2x-8)/x^2-16

Factor the numerator and denominator.

\(\frac{x^2-2x-8}{x^2-16}=\frac{(x-4)(x+2)}{(x-4)(x+4)}\)

Now it is easy to see that if x = -4 or +4, the denominator will = 0.

(If it wasn't easy to see, just set the denominator equal to zero and solve for x.)

So there is a restriction that x  ≠ ± 4

Now reduce the numerator and denominator by (x - 4) .

\(\frac{(x-4)(x+2)}{(x-4)(x+4)}=\frac{(x+2)}{(x+4)} \\~\\ \frac{x+2}{x+4}\)

Now it is simplified, and the only restriction is x  ≠ ± 4