Question

Solve:
$\frac{1}{x+4}+\frac{1}{x-4}=1$

Answer 1

$\frac{1}{x+4}+\frac{1}{x-4}=1$

$\Rightarrow \frac{x-4+x+4}{x^2-16}=1$

$\Rightarrow 2x=x^2-16$

$\Rightarrow x^2-2x-16=0$

$\Rightarrow x^2-2\times x\times 1+1-1-16=0$

$\Rightarrow {(x-1)}^2-17=0$

$\Rightarrow {(x-1)}^2=17$

$\Rightarrow x-1=\pm \sqrt{17}$

$\therefore x=1\pm \sqrt{17}$