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

Problem 1.247 · medium

1. \[ \lim_{x \to \frac{1}{2}^+}\left(\frac{2 x + 1}{2 x - 3}\right) \]
   limitStart with the original limit expression.✓ Proved
2. \[ = \lim_{x \to \frac{1}{2}^+}\left(2 x + 1\right) \left(\lim_{x \to \frac{1}{2}^+}\left(2 x - 3\right)\right)^{-1} \]
   limit-lawApply the quotient rule for limits.✓ Proved
3. \[ = -1 \]
   substitution algebra algebra algebraSubstitute the value x = 1/2 into the expression. Simplify the terms in the numerator and denominator. Perform the addition and subtraction. Divide the numerator by the denominator.✓ Proved