Limit of \( \displaystyle \frac{9 x^{2} - 9}{3 x + 3} \) as \( x \to -1 \)

Problem 1.324 · medium

1. \[ \lim_{x \to -1^+}\left(\frac{9 x^{2} - 9}{3 x + 3}\right) \]
   limit factorStart with the limit of the given function. Factor the numerator.✓ Proved
2. \[ = \lim_{x \to -1^+}\left(\frac{\left(x + 1\right) \left(9 x - 9\right)}{3 x + 3}\right) \]
   factor factorFactor the difference of squares. Factor the denominator.✓ Proved
3. \[ = \lim_{x \to -1^+}\left(3 x - 3\right) \]
   simplifyCancel the common factor (x + 1).✓ Proved
4. \[ = -6 \]
   limit simplifyEvaluate the expression at x = -1. Final result.✓ Proved