(x^2-1)/(x-1) Simplify

Jasonbradley

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Jun 17, 2024

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Simplifying the Expression (x² - 1) / (x - 1)

This expression can be simplified by factoring the numerator and then cancelling common factors. Here's how:

1. Factor the numerator

The numerator (x² - 1) is a difference of squares, which can be factored as follows:

x² - 1 = (x + 1)(x - 1)

2. Rewrite the expression

Now we can rewrite the original expression with the factored numerator:

(x² - 1) / (x - 1) = (x + 1)(x - 1) / (x - 1)

3. Cancel common factors

Notice that both the numerator and denominator share the factor (x - 1). We can cancel this factor:

(x + 1)(x - 1) / (x - 1) = x + 1

Important Note:

It's crucial to remember that this simplification is only valid when x ≠ 1. This is because if x = 1, the original expression becomes undefined (division by zero).

Therefore, the simplified expression is x + 1, where x ≠ 1.