\(\begin{array}{l}
a)\,\,\frac{{25\left( {x - 2} \right)}}{{20x\left( {2 - x} \right)}} = \frac{{ - 25\left( {2 - x} \right)}}{{20x\left( {2 - x} \right)}} = \frac{{ - 5}}{{4x}}.\\
b)\,\,\frac{{x{{\left( {4 - x} \right)}^2}}}{{x - 4}} = \frac{{x{{\left( {x - 4} \right)}^2}}}{{x - 4}} = x\left( {x - 4} \right).\\
c)\,\,\frac{{{{\left( {x - y} \right)}^2}}}{{x{{\left( {y - x} \right)}^3}}} = \frac{{{{\left( {y - x} \right)}^2}}}{{x{{\left( {y - x} \right)}^3}}} = \frac{1}{{x\left( {y - x} \right)}}.\\
d)\,\,\frac{{x\left( {x - 2} \right)}}{{{{\left( {2 - x} \right)}^3}}} = - \frac{{x\left( {x - 2} \right)}}{{{{\left( {x - 2} \right)}^3}}} = - \frac{x}{{{{\left( {x - 2} \right)}^2}}}.
\end{array}\)
