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The question in the image asks, "Za katero vrednost \(x\) dani ulomek ni določen?" which translates to "For which value of \(x\) is the given fraction undefined?" This indicates that we need to determine where the denominators of the fractions equal zero, as fractions are undefined when their denominators are zero.

Let’s solve each expression one by one:

1. **a) \(\frac{1 + x}{x^2 - 1}\)**
   - The denominator is \(x^2 - 1 = (x - 1)(x + 1)\). 
   - The fraction is undefined when \(x^2 - 1 = 0\), i.e., \(x = \pm 1\).

2. **b) \(\frac{2x}{5}\)**
   - The denominator is 5, which is a constant and never zero.
   - The fraction is always defined for all values of \(x\).

3. **c) \(\frac{3x - 6}{x^2 - 9}\)**
   - The denominator is \(x^2 - 9 = (x - 3)(x + 3)\).
   - The fraction is undefined when \(x = \pm 3\).

4. **d) \(\frac{x(x - 1)}{5}\)**
   - The denominator is 5, which is a constant and never zero.
   - The fraction is always defined for all values of \(x\).

5. **e) \(\frac{7x^2}{(x - 4)^2}\)**
   - The denominator is \((x - 4)^2\), which is zero when \(x = 4\).
   - The fraction is undefined when \(x = 4\).

6. **f) \(\frac{5}{x^2 + 10x + 25}\)**
   - The denominator is \(x^2 + 10x + 25 = (x + 5)^2\).
   - The fraction is undefined when \(x = -5\).

### Summary of when the fractions are undefined:
- a) Undefined for \(x = 1\) and \(x = -1\).
- b) Always defined.
- c) Undefined for \(x = 3\) and \(x = -3\).
- d) Always defined.
- e) Undefined for \(x = 4\).
- f) Undefined for \(x = -5\).

Would you like further clarification or detailed steps for any of these? Here are five related questions:

1. How do you find the values of \(x\) where a rational function is undefined?
2. Can you simplify a rational expression before determining when it's undefined?
3. What are the properties of the denominator in a rational expression?
4. What happens to the graph of a rational function at values where it is undefined?
5. How do you solve for roots in polynomial denominators?

**Tip**: Always factor the denominator of a fraction to find when it equals zero!

Za katero vrednost x dani ulomek ni določen? (For which value of x is the given fraction undefined?)

Discover how to find values of x where rational expressions are undefined by determining when the denominator equals zero. This problem involves factoring and rational functions, suitable for Grades 9-11 students.

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