Giải phương trình 2(x + 1)/x + 2 = x^2 + x + 8/(x + 2)(x - 3)

* Hướng dẫn giải

$\frac{2(x+1)}{x+2}=\frac{x^2+x+8}{\left(x+2\right)\left(x-3\right)}\left(\begin{array}{l}x\ne -2\\ x\ne 3\end{array}\right)$

$\begin{array}{l}\iff \frac{2\left(x+1\right)\left(x-3\right)}{\left(x+2\right)\left(x-3\right)}=\frac{x^2+x+8}{\left(x+2\right)\left(x-3\right)}\\ \Rightarrow 2x^2-4x-6=x^2+x+8\iff x^2-5x-14=0\iff \left[\begin{array}{l}x=7(t/m)\\ x=-2\left(loai\right)\end{array}\right.\\ S=\left\{7\right\}\end{array}$