To determine the value of [tex]\( x \)[/tex] that makes the expression [tex]\(\frac{1}{x-3}\)[/tex] undefined, follow these steps:
1. Identify the Denominator of the Expression:
The expression given is [tex]\(\frac{1}{x-3}\)[/tex]. The denominator here is [tex]\(x-3\)[/tex].
2. Set the Denominator Equal to Zero:
For the expression to be undefined, the denominator must be zero because division by zero is undefined in mathematics. So, we set up the equation:
[tex]\[
x - 3 = 0
\][/tex]
3. Solve the Equation for [tex]\( x \)[/tex]:
Solve the equation by isolating [tex]\( x \)[/tex]:
[tex]\[
x - 3 = 0 \implies x = 3
\][/tex]
Thus, the expression [tex]\(\frac{1}{x-3}\)[/tex] is undefined when [tex]\( x = 3 \)[/tex].
Answer: The value of [tex]\( x \)[/tex] that makes the expression [tex]\(\frac{1}{x-3}\)[/tex] undefined is:
[tex]\[
\boxed{3}
\][/tex]
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