RATIONAL EXPRESSIONS Restriction on a variable in a denominator: Quadratic
Find all excluded values for the expression.
That is, find all values of $x$ for which the expression is undefined.
\[
\frac{x^{2}-6 x+8}{x^{2}-1}
\]
If there is more than one value, separate them with commas.
\[
x=
\]
Answer
The excluded values for the expression are $x=-1$ and $x=1$. So, $x=\boxed{-1, 1}$.
Step 1 ：The expression is undefined when the denominator equals zero. So, we need to find the values of $x$ that make $x^{2}-1=0$. This is a quadratic equation, and we can solve it by factoring or using the quadratic formula.
Step 2 ：The solutions to the equation $x^{2}-1=0$ are $x=-1$ and $x=1$. These are the values of $x$ that make the denominator zero and thus make the expression undefined.
Step 3 ：The excluded values for the expression are $x=-1$ and $x=1$. So, $x=\boxed{-1, 1}$.
