Simplify the given polynomial expression: 2. $\left(x^{2}-5 x+6\right)-\left(2 x^{2}-x-3\right)$

Step 1 ：Distribute the negative sign to the terms in the second parentheses: \(x^{2}-5x+6 - (2x^{2}-x-3)\) becomes \(x^{2}-5x+6 -2x^{2}+x+3\).

Step 2 ：Combine like terms: \(x^{2}-5x+6 -2x^{2}+x+3\) becomes \(-x^{2} - 4x + 9\).

Step 3 ：\(\boxed{-x^{2} - 4x + 9}\) is the final simplified form of the given polynomial expression.