Lời giải:
a) ĐKXĐ: \(\left\{\begin{matrix} x\neq 0\\ x-1\neq 0\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix} x\neq 0\\ x\neq 1\end{matrix}\right.\)
b)
\(A=\frac{-1}{x(x-1)}-\frac{2}{x}+\frac{x}{x-1}=\frac{-1}{x(x-1)}-\frac{2(x-1)}{x(x-1)}+\frac{x^2}{x(x-1)}\)
\(=\frac{-1-2(x-1)+x^2}{x(x-1)}=\frac{x^2-2x+1}{x(x-1)}=\frac{(x-1)^2}{x(x-1)}=\frac{x-1}{x}\)
c)
Khi \(x^2-9x+20=0\)
\(\Leftrightarrow (x-4)(x-5)=0\Rightarrow \left[\begin{matrix} x=4\\ x=5\end{matrix}\right.\)
Với $x=4$ thì \(A=\frac{4-1}{4}=\frac{3}{4}\)
Với $x=5$ thì \(A=\frac{5-1}{5}=\frac{4}{5}\)