Quadratic Functions, Equations and Inequalities - Evaluating Expressions using Special Identities

Given that \({{x}^{2}}-5x-2025=0\), find the value of \(\frac{{{\left( x-2 \right)}^{4}}+{{\left( x-1 \right)}^{2}}-1}{\left( x-1 \right)\left( x-2 \right)}\).