Giải các phương trình sau : a. (3x-1)/(x-1)-(2x+5)/(x+3)=1-4/(x-1)(x+3)

* Hướng dẫn giải

$\begin{array}{l}\frac{3x-1}{x-1}-\frac{2x+5}{x+3}=1-\frac{4}{\left(x-1\right)\left(x+3\right)}\left(\begin{array}{l}x\ne 1\\ x\ne -3\end{array}\right)\\ \iff \frac{\left(3x-1\right)\left(x+3\right)-\left(2x+5\right)\left(x-1\right)}{\left(x-1\right)\left(x+3\right)}=\frac{\left(x-1\right)\left(x+3\right)-4}{\left(x-1\right)\left(x+3\right)}\\ \Rightarrow 3x^2+8x-3-2x^2-3x+5=x^2+2x-3-4\\ \iff 3x=-9\iff x=-3\left(ktm\right)S=\varnothing \end{array}$