What is the simplified form of the rational expression (x² - 1)/(x - 1)?

To simplify the rational expression ((x^2 - 1)/(x - 1)), it’s essential to first factor the numerator. The expression (x^2 - 1) is a difference of squares, which can be factored as ((x - 1)(x + 1)).

Thus, the original expression can be rewritten as:

[

\frac{(x - 1)(x + 1)}{(x - 1)}

]

As long as (x \neq 1) (to avoid division by zero), the ((x - 1)) terms in the numerator and the denominator can be canceled. This simplification leaves us with:

[

x + 1

]

This means that the simplified form of the given rational expression is (x + 1). Hence, this is the correct response in this context. Understanding this process involves factoring and recognizing the importance of excluding values that could lead to undefined expressions in rational functions.