A. Non-Permissible Values and Extraneous Roots
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A. Non-Permissible Values and Extraneous Roots
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The first step in simplifying rational expressions is to identify any non-permissible values; the importance of this step is even more significant when solving rational equations. After simplifying a rational expression, one or more of the factors in the denominator may have been eliminated, but the eliminated factor still contributes to the list of non-permissible values. When solving rational equations, you may end up with one or more answers that are non-permissible values. These are extraneous roots, similar to those found in Unit 3: Radicals, where a solution is found algebraically, but not valid when substituted into the original equation.