What is the domain of $$ f(x)=\frac{x^{2}-3 x+2}{x^{2}-1} ? $$ $$ x=\mathbb{R}, x
eq 1 $$ $$ x=\mathbb{R}, x
eq 1, x
eq-1 $$ $$ x=\mathbb{R}, x
eq 3 $$ $$ x \geq 0 $$ $$ x \geq 1 $$

Question

What is the domain of $$ f(x)=\frac{x^{2}-3 x+2}{x^{2}-1} ? $$ $$ x=\mathbb{R}, x 
eq 1 $$ $$ x=\mathbb{R}, x 
eq 1, x 
eq-1 $$ $$ x=\mathbb{R}, x 
eq 3 $$ $$ x \geq 0 $$ $$ x \geq 1 $$

UpStudy AI · Accepted Answer

To determine the domain of the function $$ f(x) = \frac{x^{2} - 3x + 2}{x^{2} - 1} $$, we need to identify all real numbers $$ x $$ for which the denominator is not zero, as division by zero is undefined.

### Step-by-Step Analysis:

1. **Identify the Denominator:**
   $$
   \text{Denominator} = x^{2} - 1
   $$

2. **Find the Values that Make the Denominator Zero:**
   $$
   x^{2} - 1 = 0 \implies x^{2} = 1 \implies x = \pm 1
   $$
   So, $$ x = 1 $$ and $$ x = -1 $$ are the values that make the denominator zero.

3. **Determine the Domain:**
   The domain consists of all real numbers except those that make the denominator zero. Therefore, the domain is:
   $$
   x \in \mathbb{R} \quad \text{such that} \quad x \neq 1 \quad \text{and} \quad x \neq -1
   $$

### Conclusion:

Among the provided options, the correct domain excludes both $$ x = 1 $$ and $$ x = -1 $$.

**Answer:** 
$$ x =\mathbb{R}, x \neq 1, x \neq-1 $$
The domain of $$ f(x) $$ is all real numbers except $$ x = 1 $$ and $$ x = -1 $$.

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