Limit of \( \displaystyle \frac{8 x^{2} - 6 x - 2}{2 x - 2} \) as \( x \to 1 \)

Problem 1.222 · medium

1. \[ \lim_{x \to 1^+}\left(\frac{8 x^{2} - 6 x - 2}{2 x - 2}\right) \]
   limit factorStart with the limit of the given function. Factor the numerator.✓ Proved
2. \[ = \lim_{x \to 1^+}\left(\frac{\left(x - 1\right) \left(8 x + 2\right)}{2 x - 2}\right) \]
   factorFactor the quadratic expression further.✓ Proved
3. \[ = \lim_{x \to 1^+}\left(4 x + 1\right) \]
   simplify cancelSimplify the constant factor 2/2. Cancel the common factor (x - 1).✓ Proved
4. \[ = 5 \]
   limitEvaluate the limit by substitution.✓ Proved