Limit of (x^2 - 4) / (x^2 - x - 2) as x approaches 2

Math Problem Statement

Find the limit of $ \lim_{x \to 2} \frac{x^2 - 4}{x^2 - x - 2} $

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The equation appears to be: $\lim_{x \to 2} \frac{x^2 - 4}{x^2 - x - 2}$

To solve this, let's first simplify the expression step by step.

We need to factor both the numerator and the denominator.

The numerator $x^2 - 4$ is a difference of squares, which can be factored as: $x^2 - 4 = (x - 2)(x + 2)$
The denominator $x^2 - x - 2$ factors as: $x^2 - x - 2 = (x - 2)(x + 1)$

Now the expression becomes: $\frac{(x - 2)(x + 2)}{(x - 2)(x + 1)}$ We can cancel the common factor $x - 2$ , as long as (

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Limits
Factorization
Algebra

Difference of squares
Limit calculation by factoring

Limit cancellation theorem

Grades 10-12

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