Solve lim x→2 of (x²-4)/(x-2)

Problem

$\lim_{x \to 2} \frac{x^2 - 4}{x - 2}$

Step-by-step solution

Direct substitution gives $\frac{0}{0}$ — indeterminate.
Factor numerator as difference of squares: $x^2 - 4 = (x - 2)(x + 2)$ .
Cancel the common factor $(x - 2)$ : $\lim_{x \to 2}(x + 2)$ .
Substitute: $2 + 2 = 4$ .

Answer

$4$

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