Giải phương trình x + 4/x^2 - 3x + 2 + x + 1/x^2 - 4x + 3 = 2x + 5/x^2 - 4x + 3

* Hướng dẫn giải

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

$\begin{array}{l}\Rightarrow \left(x+4\right)\left(x-1\right)\left(x-3\right)-\left(x+4\right)\left(x-1\right)\left(x-2\right)=0\\ \iff \left(x+4\right)\left(x-1\right)\left(x-3-x+2\right)=0\iff \left[\begin{array}{l}x=-4\left(tm\right)\\ x=1\left(ktm\right)\end{array}\right.\end{array}$