Limit of \( \displaystyle \frac{- 15 x + \left(3 x - 1\right)^{2} + 11}{3 x - 4} \) as \( x \to \frac{4}{3} \)

Problem 1.329 · medium

1. \[ \lim_{x \to \frac{4}{3}^+}\left(\frac{- 15 x + \left(3 x - 1\right)^{2} + 11}{3 x - 4}\right) \]
   limitEvaluate the limit of the given function.✓ Proved
2. \[ = \lim_{x \to \frac{4}{3}^+}\left(\frac{9 x^{2} - 21 x + 12}{3 x - 4}\right) \]
   simplify simplify factorExpand the squared term. Combine like terms in the numerator. Factor out the common constant 3.✓ Proved
3. \[ = \lim_{x \to \frac{4}{3}^+}\left(\frac{\left(x - 1\right) \left(9 x - 12\right)}{3 x - 4}\right) \]
   factorFactor the quadratic expression in the numerator.✓ Proved
4. \[ = \lim_{x \to \frac{4}{3}^+}\left(3 x - 3\right) \]
   cancelCancel the common factor (3*x - 4).✓ Proved
5. \[ = 1 \]
   limit simplifySubstitute the value x = 4/3 into the simplified expression. Calculate the final value.✓ Proved