Question

For what values of the variable is the rational expression undefined? $$\frac{x-1}{x-5}$$

Short answer

The rational expression is undefined when \(x = 5\).

Step-by-step solution

- Identify the Denominator

In the given rational expression \(\frac{x-1}{x-5}\), the denominator is \(x - 5\).

- Set the Denominator Equal to Zero and Solve for x

In order for the expression to be undefined, the denominator should equal zero. So, we set \(x - 5 = 0\). Solving for x, we add 5 to both sides to get \(x = 5\).