What is the domain of the function `(x)/(x^(2) - 3x + 2)` ?

Answer

To find the domain of the function \( f(x) = \frac{x}{x^2 - 3x + 2} \), we need to determine the values of \( x \) for which the function is defined. The function is undefined when the denominator is equal to zero.

### Step-by-Step Solution:

1. **Identify the function**:
The function is given as:
\[ f(x) = \frac{x}{x^2 - 3x + 2} \]

2. **Set the denominator to zero**:
To find when the function is undefined, we set the denominator equal to zero:
\[ x^2 - 3x + 2 = 0 \]

3. **Factor the quadratic equation**:
We can factor the quadratic expression:
\[ x^2 - 3x + 2 = (x - 1)(x - 2) \]
This means the equation can be rewritten as:
\[ (x - 1)(x - 2) = 0 \]

4. **Find the roots**:
Setting each factor to zero gives us the values of \( x \) that make the denominator zero:
\[ x - 1 = 0 \quad \Rightarrow \quad x = 1 \]
\[ x - 2 = 0 \quad \Rightarrow \quad x = 2 \]

5. **Determine the domain**:
The function is undefined at \( x = 1 \) and \( x = 2 \). Therefore, the domain of the function is all real numbers except these two values:
\[ \text{Domain of } f(x) = \{ x \in \mathbb{R} \mid x \neq 1, x \neq 2 \} \]

### Final Answer:
The domain of the function \( f(x) = \frac{x}{x^2 - 3x + 2} \) is:
\[ \text{Domain} = \mathbb{R} \setminus \{1, 2\} \]