\(a,A=\dfrac{x^4-4x^3+4x^2}{x^3-4x}\)
\(\Rightarrow A=\dfrac{x^2\left(x^2-4x+4\right)}{x\left(x^2-4\right)}\)
\(\Rightarrow A=\dfrac{x^2\left(x-2\right)^2}{x\left(x-2\right)\left(x+2\right)}\)
\(\Rightarrow A=\dfrac{x\left(x-2\right)}{x+2}\)
\(b,A=0\Leftrightarrow\dfrac{x\left(x-2\right)}{x+2}=0\\ \Leftrightarrow x\left(x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)