Limit of \( \displaystyle \frac{- 6 x + 2 \left(2 x - 1\right)^{2} + 1}{2 x - 3} \) as \( x \to \frac{3}{2} \)

Problem 1.303 · hard

1. \[ \lim_{x \to \frac{3}{2}^+}\left(\frac{- 6 x + 2 \left(2 x - 1\right)^{2} + 1}{2 x - 3}\right) \]
   limit algebraEvaluate the limit of the given function at x = 3/2. Rearrange the terms in the numerator.✓ Proved
2. \[ = \lim_{x \to \frac{3}{2}^+}\left(\frac{8 x^{2} - 14 x + 3}{2 x - 3}\right) \]
   simplifyExpand the squared binomial and combine like terms.✓ Proved
3. \[ = \lim_{x \to \frac{3}{2}^+}\left(4 x - 1\right) \]
   factor cancelFactor the quadratic expression in the numerator. Cancel the common factor (2*x - 3) from the numerator and denominator.✓ Proved
4. \[ = 5 \]
   limitEvaluate the remaining expression at x = 3/2.✓ Proved