Problem 4 - Introductory Algebra for College Students

Question

Find all numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state. $$\frac{x}{x-6}$$

Step-by-Step Solution

Answer

The given rational expression \( \frac{x}{x-6} \) is undefined at x = 6.

Step 1: Identify the Denominator

Look at the given expression \( \frac{x}{x-6} \). Identify the denominator, which in this case, is (x - 6).

Step 2: Set the Denominator Equal to Zero

Set the denominator equal to zero. So, write down the equation in the following form: x-6 = 0.

Step 3: Solve the equation

Move -6 to the other side by adding 6 to both sides of the equation. This results in x=6.