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The question is asking for which value makes the given expression \(\frac{x^2 - 4x + 5}{x - 2}\) undefined.

An expression becomes undefined when the denominator is equal to zero. So, we need to set the denominator \(x - 2 = 0\) and solve for \(x\).

\[
x - 2 = 0
\]
\[
x = 2
\]

Thus, the expression is undefined when \(x = 2\).

Would you like further explanation or have any questions about this problem?

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Here are 5 related questions for practice:

1. What is the domain of the function \(f(x) = \frac{x^2 - 4x + 5}{x - 2}\)?
2. Can the numerator \(x^2 - 4x + 5\) be factored further?
3. What happens to the value of the expression when \(x = 2\)?
4. How would you simplify a similar rational expression where the denominator has more complex factors?
5. How do you find vertical asymptotes in rational functions like this?

**Tip:** To determine when a rational function is undefined, always check the values of \(x\) that make the denominator zero.

Which among the following values makes \( \frac{x^2 - 4x + 5}{x - 2} \) undefined?

Learn how to determine when the rational expression \( \frac{x^2 - 4x + 5}{x - 2} \) becomes undefined by solving for the value of x that makes the denominator zero. This concept is key for students in Grades 8-10 studying algebra and rational functions.

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