Question

For what values of the variable is the rational expression undefined? $$\frac{6}{8 x}$$

Short answer

The rational expression is undefined for \(x = 0\).

Step-by-step solution

Identify the Denominator

In this rational expression, the denominator is \(8x\). So any value of \(x\) that makes the denominator equal to zero will create a situation where division by zero occurs. Thus, we need to find the solution to the equation \(8x = 0\).

Solve the Equation

Setting the denominator equal to zero and simplifying, we find: \[8x = 0 \Rightarrow x = \frac{0}{8} \Rightarrow x = 0\]