Problem 71 - College Algebra

Question

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

Step-by-Step Solution

Answer

To find which numbers to exclude from the domain of a rational expression, set the denominator equal to zero and solve for x. The solutions are the numbers that must be excluded from the domain because they make the denominator equal to zero and the expression undefined.

Step 1: Identify the Denominator

Inspect the rational expression, identify the denominator part of the expression.

Step 2: Set the denominator equal to zero

Take the denominator of the rational expression and set it equal to zero, this will give you an equation to solve.

Step 3: Solve for x

Solve the equation obtained in the previous step. This will provide the values of x (variable) that make the denominator equal to zero.

Step 4: List the Excluded Values

The solution(s) to the equation are the values that must be excluded from the domain of the rational expression. These are the values that, when substituted back into the original expression, would make the denominator equal to zero.