\(\Leftrightarrow\frac{5\left(x-1\right)}{x^2-4x+6}+\frac{6\left(x-1\right)}{x^2-5x+7}=\frac{17}{2}\)
\(\Leftrightarrow\frac{5\left(x^2-4x+6-x^2+5x-7\right)}{x^2-4x+6}+\frac{6\left(x^2-4x+6-x^2+5x-7\right)}{x^2-5x+7}=\frac{17}{2}\)
\(\Leftrightarrow5-\frac{5\left(x^2-5x+7\right)}{x^2-4x+6}+\frac{6\left(x^2-4x+6\right)}{x^2-5x+7}-6=\frac{17}{2}\)
\(\Leftrightarrow\frac{6\left(x^2-4x+6\right)}{x^2-5x+7}-\frac{5\left(x^2-5x+7\right)}{x^2-4x+6}-\frac{19}{2}=0\)
Đặt \(\frac{x^2-4x+6}{x^2-5x+7}=a\)
\(\Leftrightarrow6a-\frac{5}{a}-\frac{19}{2}=0\Leftrightarrow12a^2-19a-10=0\) \(\Rightarrow\left[{}\begin{matrix}a=2\\a=-\frac{5}{12}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\frac{x^2-4x+6}{x^2-5x+7}=2\\\frac{x^2-4x+6}{x^2-5x+7}=-\frac{5}{12}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x^2-6x+8=0\\17x^2-73x+107=0\left(vn\right)\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=2\\x=4\end{matrix}\right.\)