Problem 87 - Algebra and Trigonometry

Question

Explain how to determine which numbers must be excluded from the domain of a rational expression.

Step-by-Step Solution

Answer

The numbers to be excluded from the domain of a rational expression are the values of the variable that make the denominator of the expression equal to zero, because division by zero is undefined.

Step 1: Identify the Denominator of the Rational Expression

The first step is to identify the denominator of the rational expression. This is the part of the expression that's located below the division line.

Step 2: Set the Denominator Equal to Zero

This step involves setting the denominator equal to zero. The reason for this is that any value of the variable that makes the denominator equal to zero will be excluded from the domain.

Step 3: Solve for the Variable

After setting the denominator equal to zero, solve the resulting equation for the variable. The derived values are the numbers to be excluded from the domain, because if they were included in the domain, they would make the denominator zero and the expression undefined.