Tính \(f(x)\) biết hàm số \(f\left( x \right) = \frac{{x - 2}}{{x - 1}}\).

A. \(f'\left( x \right) = \frac{1}{{{{\left( {x - 1} \right)}^2}}}\)

B. \(f'\left( x \right) = \frac{2}{{{{\left( {x - 1} \right)}^2}}}\)

C. \(f'\left( x \right) = \frac{-2}{{{{\left( {x - 1} \right)}^2}}}\)

D. \(f'\left( x \right) = \frac{-1}{{{{\left( {x - 1} \right)}^2}}}\)