Chapter 11.1, Problem 5LC

To determine

Explain why we exclude the values when simplifying the rational expression.

Explanation of Solution

Rational expression is in the form $\frac{\text{P}}{\text{Q}}$ , where $\text{Q}\ne 0$ , denominator cannot be zero in any rational expression.

The denominator in a rational expression cannot be zero because division by zero is undefined. So we need to figure out what values of the variable(s) in the expression would make the denominator equal zero. These values cannot be included in the domain, so they're called excluded values.

Excluded values are also called points of discontinuity. These are the values that make the denominator equal to zero and are not part of the domain.