We are asked to simplify the expression:

$\frac{2x^2 - 10x}{x^2 - 1}$

Step 1: Factor the numerator and denominator

Factor the numerator:

The numerator is $2x^2 - 10x$. We can factor out a common factor of 2x:

$2x^2 - 10x = 2x(x - 5)$

Factor the denominator:

The denominator is $x^2 - 1$, which is a difference of squares. We can factor it as:

$x^2 - 1 = (x - 1)(x + 1)$

Step 2: Rewrite the expression

Now, we can rewrite the expression with the factored forms:

$\frac{2x(x - 5)}{(x - 1)(x + 1)}$

Step 3: Check for any common factors

There are no common factors between the numerator and the denominator, so the expression cannot be simplified further.

Thus, the simplified expression is:

$\frac{2x(x - 5)}{(x - 1)(x + 1)}$

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Would you like more details on any of the steps, or do you have another question?

Here are some related questions you can explore:

1. How do you factor a quadratic expression like $x^2 - 1$?
2. What is the difference of squares formula, and how does it help in factoring?
3. How do you simplify rational expressions with common factors?
4. What are some examples of factoring out the greatest common factor (GCF)?
5. How do you handle division and multiplication of rational expressions?

Tip: Always check for common factors first to simplify the expression as much as possible!