Giải phương trình 1/(x+4)(x+5)+1/(x+5)(x+6)+1/(x+6)(x+7)=1/18

* Hướng dẫn giải

$\begin{array}{l}\frac{1}{\left(x+4\right)\left(x+5\right)}+\frac{1}{\left(x+5\right)\left(x+6\right)}+\frac{1}{\left(x+6\right)\left(x+7\right)}=\frac{1}{18}\left(x\ne -4;-5;-6;-7\right)\\ \iff \frac{1}{x+4}-\frac{1}{x+5}+\frac{1}{x+5}-\frac{1}{x+6}+\frac{1}{x+6}-\frac{1}{x+7}=\frac{1}{18}\iff \frac{1}{x+4}-\frac{1}{x+7}=\frac{1}{18}\\ \iff \frac{x+7-x-4}{\left(x+4\right)\left(x+7\right)}=\frac{1}{18}\iff x^2+11x-26=0\iff \left[\begin{array}{l}x=2\\ x=-13\end{array}\right.\left(tm\right)\end{array}$