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

Problem 1.84 · medium

1. \[ \lim_{x \to 3^+}\left(\frac{- 3 x + 2 \left(x - 1\right)^{2} + 1}{x - 3}\right) \]
   limitStart with the limit of the given function.✓ Proved
2. \[ = \lim_{x \to 3^+}\left(\frac{2 x^{2} - 7 x + 3}{x - 3}\right) \]
   simplifySimplify the numerator.✓ Proved
3. \[ = \lim_{x \to 3^+}\left(\frac{\left(x - \frac{1}{2}\right) \left(2 x - 6\right)}{x - 3}\right) \]
   factorFactor the numerator to reveal the common factor.✓ Proved
4. \[ = \lim_{x \to 3^+}\left(2 x - 1\right) \]
   cancelCancel the common factor (x - 3).✓ Proved
5. \[ = 5 \]
   limitEvaluate the limit by substituting x = 3.✓ Proved