Limit of \( \displaystyle \frac{9 x^{2} + 3 x - 6}{3 x - 2} \) as \( x \to \frac{2}{3} \)

Problem 1.143 · medium

1. \[ \lim_{x \to \frac{2}{3}^+}\left(\frac{9 x^{2} + 3 x - 6}{3 x - 2}\right) \]
   limit factorEvaluate the limit of the given function at x = 2/3. Factor out 3 from the numerator.✓ Proved
2. \[ = \lim_{x \to \frac{2}{3}^+}\left(\frac{\left(x + 1\right) \left(9 x - 6\right)}{3 x - 2}\right) \]
   factorFactor the quadratic expression 3*x**2 + x - 2.✓ Proved
3. \[ = \lim_{x \to \frac{2}{3}^+}\left(3 x + 3\right) \]
   cancelCancel the common factor (3*x - 2) from the numerator and denominator.✓ Proved
4. \[ = 5 \]
   limit simplify simplifySubstitute x = 2/3 into the simplified expression. Combine the terms inside the parentheses. Multiply the remaining terms.✓ Proved