O. Simplify the expression. \[ \frac{2 x^{2}-11 x+5}{2 x-1} \]

To simplify the expression \(\frac{2 x^{2}-11 x+5}{2 x-1}\), we start by factoring the numerator. We want to express \(2x^2 - 11x + 5\) in a form that reveals its factors. By using the factoring technique, we find that: \[2x^2 - 11x + 5 = (2x - 1)(x - 5).\] Now substituting this back into the expression gives us: \[ \frac{(2x - 1)(x - 5)}{2x - 1}. \] As long as \(2x - 1 \neq 0\) (or \(x \neq \frac{1}{2}\)), we can cancel out \(2x - 1\) from the numerator and denominator: \[ x - 5. \] Thus, the simplified expression is: \[ x - 5 \quad \text{for } x \neq \frac{1}{2}. \]