Factorise the inequality
#(x^2-2x-24)/(x^2-8x-20)=((x+4)(x-6))/((x+2)(x-10))>=0#
Let #f(x)=((x+4)(x-6))/((x+2)(x-10))#
Perform a sign chart
#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##-4##color(white)(aaaa)##-2##color(white)(aaaaa)##6##color(white)(aaaa)##10##color(white)(aaaa)##+oo###
#color(white)(aaaa)##x+4##color(white)(aaaaa)##-##color(white)(aa)##0##color(white)(aaa)##+##color(white)(aaa)##+##color(white)(aaa)##+##color(white)(aaa)##+###
#color(white)(aaaa)##x+2##color(white)(aaaaa)##-##color(white)(aa)####color(white)(aaaa)##-##color(white)(a)##||##color(white)(a)##+##color(white)(aaa)##+##color(white)(aaa)##+#
#color(white)(aaaa)##x-6##color(white)(aaaaa)##-##color(white)(aa)####color(white)(aaaa)##-##color(white)(a)####color(white)(aa)##-##color(white)(a)##0##color(white)(a)##+##color(white)(aaa)##+#
#color(white)(aaaa)##x-10##color(white)(aaaa)##-##color(white)(aa)####color(white)(aaaa)##-##color(white)(a)####color(white)(aa)##-##color(white)(a)####color(white)(aa)##-##color(white)(a)##||##color(white)(a)##+#
#color(white)(aaaa)##f(x)##color(white)(aaaaaa)##+##color(white)(aa)##0##color(white)(aaa)##-##color(white)(a)##||##color(white)(a)##+##color(white)(a)##0##color(white)(a)##-##color(white)(a)##||##color(white)(a)##+#
Therefore,
#f(x)>=0# when #x in (-oo,-4] uu (-2, 6] uu (10, +oo)#
graph{(x^2-2x-24)/(x^2-8x-20) [-25.65, 25.66, -12.83, 12.84]}