Giải phương trình (x-1)/(x-2)+(3-x)/(x-4)

* Hướng dẫn giải

$\begin{array}{l}\frac{x-1}{x-2}+\frac{3-x}{x-4}=\frac{-2x}{\left(x-2\right)\left(x-4\right)}\left(\begin{array}{l}x\ne 2\\ x\ne 4\end{array}\right)\\ \iff \frac{\left(x-1\right)\left(x-4\right)+\left(3-x\right)\left(x-2\right)}{\left(x-2\right)\left(x-4\right)}=\frac{-2x}{\left(x-2\right)\left(x-4\right)}\\ \Rightarrow x^2-5x+4-x^2+5x-6+2x=0\iff x=1\left(tm\right)\end{array}$