\frac{2}{x+1}+\frac{5}{x-2}=-2
\frac{2}{x+1}+\frac{5}{x-2}+2=0
\frac{2(x-2)+5(x+1)+2(x-2)(x+1)}{(x-2)(x+1)}=0
\frac{2x-4+5x+5+2x^2-2x-4}{(x-2)(x+1)}=0
\frac{2x^2+5x-3}{(x-2)(x+1)}=0
\frac{2x^2+6x-x-3}{(x-2)(x+1)}=0
\frac{2x(x+3)-(x+3)}{(x-2)(x+1)}=0
\frac{(x+3)(2x-1)}{(x-2)(x+1)}=0
(x+3)(2x-1)=0\quad (\forall \ x\ne-1, x\ne2)
x+3=0, 2x-1=0
x=-3, 1/2