Answer
Fill the blanks with:
$x\neq-4$, ... $x\neq 2$
Work Step by Step
A solution of an equation is a value that makes the equation true.
That is, LHS=RHS after substituting x for that value.
If the value generates a zero in any denominator, then the equation is undefined.
So, that value can not be a solution.
Here, the denominators are
$x-2\qquad $so, $x\neq 2$
$x+4\qquad $so, $x\neq-4$
$x^{2}+2x-8$ is factored by searching for two factors of $c=-8$ whose sum is $b=2.$
We find $+4$ and $-2.$
$x^{2}+2x-8=(x-2)(x+4)$, so we exclude $2$ and $-4$
Fill the blanks with
$x\neq-4$, ... $x\neq 2$
