Final answer:
The expression 5/(2x-4) does not exist when x = 2, as this value makes the denominator equal to zero, thus rendering the fraction undefined.
Step-by-step explanation:
To find the values of the variable x for which the expression 5/(2x-4) does not exist, we need to determine the values that make the denominator zero. A fraction is undefined when its denominator is zero. So, we must solve the equation 2x - 4 = 0 to find when the expression is undefined.
Let's solve for x:
- Add 4 to both sides of the equation: 2x = 4.
- Divide both sides by 2: x = 2.
Therefore, the expression is undefined when x = 2, because at this value, the denominator of our fraction becomes zero.