Find the limit as x approaches 3 of (x^2 - 9)/(x - 3)

Answer

\boxed{6}

Substituting $x = 3$ directly into the original expression yields a $\frac{0}{0}$ indeterminate form, but algebraic simplification reveals the correct limit of $6$ .

Problem: Find the limit $\lim_{x \to 3} \frac{x^2 - 9}{x - 3}$ .

Steps

Factor the numerator $\lim_{x \to 3} \frac{(x - 3)(x + 3)}{x - 3}$
Cancel the common factor $\lim_{x \to 3} (x + 3)$
Substitute $x = 3$ $3 + 3 = 6$

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Find the limit as x approaches 3 of (x^2 - 9)/(x - 3)

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