Problem

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. \[ x= \]

Solution

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, $x=\boxed{-1, 1}$.

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Source: https://solvelyapp.com/problems/33728/

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