Chứng tỏ rằng P=3/x=5.

Cách giải:

$P=\left(\frac{2}{x+4}+\frac{x+20}{x^2-16}\right).\left(\frac{x-4}{x+5}\right)$ với $x\ne \pm \mathrm{4,}x\ne -5$

 $P=\left(\frac{2}{x+4}+\frac{x+20}{x^2-16}\right).\left(\frac{x-4}{x+5}\right)$ với $x\ne \pm \mathrm{4,}x\ne -5$ .

$P=\left(\frac{2}{x+4}+\frac{x+20}{x^2-16}\right).\left(\frac{x-4}{x+5}\right)$

$\begin{array}{l}=\left[\frac{2\left(x-4\right)}{\left(x+4\right)\left(x-4\right)}+\frac{x+20}{\left(x+4\right)\left(x-4\right)}\right].\left(\frac{x-4}{x+5}\right)\\ =\frac{3x+12}{\left(x+4\right)\left(x-4\right)}.\left(\frac{x-4}{x+5}\right)\\ =\frac{3\left(x+4\right)}{\left(x+4\right)\left(x-4\right)}.\left(\frac{x-4}{x+5}\right)\\ =\frac{3}{x+5}.\end{array}$

Vậy ta có điều phải chứng minh.