When working with rational expressions, it is typically assumed that all numerical values that would make the denominator equal to $$0$$ are excluded. Even if the restrictions are not explicitly written for each rational expression, it must be kept in mind that the denominator can never be zero.

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A rational expression is undefined when its denominator evaluates to $$0$$. This occurs because division by zero is mathematically undefined. While the numerator of a rational expression can be $$0$$, the denominator must never equal $$0$$. Identifying these undefined values is crucial before performing operations with rational expressions, ensuring that any algebraic solutions found later are actually allowed.

Undefined Rational Expression

https://openstax.org/details/books/intermediate-algebra-2e

OpenStax Intermediate Algebra

To determine the specific values for which a rational expression is undefined, follow these steps:
1. Set the expression in the denominator equal to $$0$$.
2. Solve the resulting equation for the variable.

The solutions obtained from this equation represent the values that make the original rational expression undefined, as they would result in division by zero.

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