\(A=\left(\dfrac{x-4}{x}-\dfrac{x}{x-4}+\dfrac{16}{x^2-4x}\right).\dfrac{x}{2x-2}\)
\(\Rightarrow A=\left(\dfrac{\left(x-4\right)^2}{x\left(x-4\right)}-\dfrac{x^2}{x\left(x-4\right)}+\dfrac{16}{x\left(x-4\right)}\right).\dfrac{x}{2\left(x-1\right)}\)
\(\Rightarrow A=\left(\dfrac{x^2-8x+16}{x\left(x-4\right)}-\dfrac{x^2}{x\left(x-4\right)}+\dfrac{16}{x\left(x-4\right)}\right).\dfrac{x}{2\left(x-1\right)}\)
\(\Rightarrow A=\dfrac{x^2-8x+16-x^2+16}{x\left(x-4\right)}.\dfrac{x}{2\left(x-1\right)}\)
\(\Rightarrow A=\dfrac{x\left(-8x+32\right)}{2x\left(x-1\right)\left(x-4\right)}\)
\(\Rightarrow A=\dfrac{-8\left(x-4\right)}{2\left(x-1\right)\left(x-4\right)}\)
\(\Rightarrow A=\dfrac{-4}{x-1}\)
\(A=\left(\dfrac{x-4}{x}-\dfrac{x}{x-4}+\dfrac{16}{x^2-4x}\right).\dfrac{x}{2x-2}=\left(\dfrac{\left(x-4\right)^2}{x\left(x-4\right)}-\dfrac{x^2}{x\left(x-4\right)}+\dfrac{16}{x\left(x-4\right)}\right).\dfrac{x}{2\left(x-1\right)}=\dfrac{x^2-8x-16-x^2+16}{x\left(x-4\right)}.\dfrac{x}{2\left(x-1\right)}=\dfrac{-8x}{x\left(x-4\right)}.\dfrac{x}{2\left(x-1\right)}=\dfrac{-4x}{\left(x-4\right)\left(x-1\right)}\)
