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To find the domain of the function \( f(x) = \frac{x^2 + x}{x - 1} \), we need to determine the values of \( x \) for which the function is defined.

### Step-by-step solution:

1. **Identify restrictions on the denominator:**
   - The function is undefined wherever the denominator equals zero, since division by zero is not allowed.
   - Here, the denominator is \( x - 1 \).

2. **Set the denominator equal to zero:**
   \[
   x - 1 = 0 \implies x = 1
   \]

3. **Determine the domain:**
   - The domain includes all real numbers except \( x = 1 \).
   - Therefore, the domain is:
     \[
     \text{Domain of } f(x): \, (-\infty, 1) \cup (1, \infty)
     \]

The function is defined for all values of \( x \) except where \( x = 1 \). 

Would you like further details or have any other questions? 

### Related Questions:
1. What is the range of the function \( f(x) = \frac{x^2 + x}{x - 1} \)?
2. How do you find the vertical asymptote of the function \( f(x) = \frac{x^2 + x}{x - 1} \)?
3. What happens to \( f(x) \) as \( x \) approaches 1?
4. How can we simplify the function \( f(x) = \frac{x^2 + x}{x - 1} \) if possible?
5. What is the behavior of \( f(x) \) as \( x \to \infty \)?

### Tip:
Always check for points where the denominator of a rational function becomes zero, as these points are excluded from the domain.

Find the domain of the function f(x) = (x^2 + x) / (x - 1).

Determine the domain of the function f(x) = (x^2 + x) / (x - 1) by identifying restrictions caused by division by zero. Understand the concept of rational functions and how to find domains in algebra. Suitable for students in Grades 9-11.

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