Chapter 11 - Section 11.3 - Solving Equations by Using Quadratic Methods - Exercise Set - Page 788: 48

$x=-12,2$

$\frac{x}{x-5}+\frac{5}{x+5}=\frac{-1}{x^2-25}$ $(x-5)(x+5)*\frac{x}{x-5}+(x-5)(x+5)*\frac{5}{x+5}=(x-5)(x+5)*\frac{-1}{x^2-25}$ $(x+5)*x+5*(x-5)=-1$ $x^2+5x+5x-25=-1$ $x^2+10x-24=0$ $(x+12)(x-2)=0$ $x+12=0$ $x=-12$ $x-2=0$ $x=2$