\(A=\frac{5x^2-10x+10-3x^2+6x-3}{x^2-2x+2}=\frac{5\left(x^2-2x+2\right)}{x^2-2x+2}-\frac{3\left(x^2-2x+1\right)}{x^2-2x+2}\)
\(A=5-\frac{3\left(x-1\right)^2}{\left(x-1\right)^2+1}\)
Do \(\left\{{}\begin{matrix}3\left(x-1\right)^2\ge0\\\left(x-1\right)^2+1>0\end{matrix}\right.\) \(\Rightarrow\frac{3\left(x-1\right)^2}{\left(x-1\right)^2+1}\ge0\) \(\forall x\)
\(\Rightarrow A\le5\)
\(\Rightarrow A_{max}=5\) khi \(x=1\)