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

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

• A. x - 1
• B. x + 1
• C. x + 2
• D. x - 2

Answer: (B)

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.

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.