Limit of \( \displaystyle \frac{- 15 x + \left(3 x + 1\right)^{2} + 1}{3 x - 2} \) as \( x \to \frac{2}{3} \)

Problem 1.499 · medium

1. \[ \lim_{x \to \frac{2}{3}^+}\left(\frac{- 15 x + \left(3 x + 1\right)^{2} + 1}{3 x - 2}\right) \]
   limitStart with the limit of the given function.✓ Proved
2. \[ = \lim_{x \to \frac{2}{3}^+}\left(\frac{9 x^{2} - 9 x + 2}{3 x - 2}\right) \]
   simplifyExpand and simplify the numerator.✓ Proved
3. \[ = \lim_{x \to \frac{2}{3}^+}\left(3 x - 1\right) \]
   factor cancelFactor the numerator to reveal the common factor. Cancel the common factor (3*x - 2).✓ Proved
4. \[ = 1 \]
   substitution limitSubstitute x = 2/3 into the simplified expression. Evaluate the final value.✓ Proved