Limit of \( \displaystyle \frac{- 5 x + \left(x - 1\right)^{2} + 11}{x - 4} \) as \( x \to 4 \)

Problem 1.111 · medium

1. \[ \lim_{x \to 4^+}\left(\frac{- 5 x + \left(x - 1\right)^{2} + 11}{x - 4}\right) \]
   limitState the original limit problem.✓ Proved
2. \[ = \lim_{x \to 4^+}\left(\frac{x^{2} - 7 x + 12}{x - 4}\right) \]
   algebra simplifyExpand the squared term. Combine like terms in the numerator.✓ Proved
3. \[ = \lim_{x \to 4^+}\left(x - 3\right) \]
   factor cancelFactor the quadratic numerator. Cancel the common factor (x - 4).✓ Proved
4. \[ = 1 \]
   limitEvaluate the limit by substitution.✓ Proved