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Find the limit as x approaches 2 of (x^2 - 4)/(x - 2)

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Answer
4\boxed{4}

Substituting x=2x = 2 directly after simplification avoids the initial 0/00/0 indeterminate form and confirms the limit is 44.

Problem: Find the limit lim⁡x→2x2−4x−2\lim_{x \to 2} \frac{x^2 - 4}{x - 2}.

Steps

  1. Factor the numerator
    lim⁡x→2(x−2)(x+2)x−2\lim_{x \to 2} \frac{(x - 2)(x + 2)}{x - 2}
  2. Cancel common factors
    lim⁡x→2(x+2)\lim_{x \to 2} (x + 2)
  3. Substitute x=2x = 2
    2+2=42 + 2 = 4

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