Question 956941
{{{F(x)=(x^2-25)/(x^2-6x-27)}}} the domain will be all real numbers excluding those which make denominator {{{(x^2-6x-27)}}} equal to zero and they are:

{{{x^2-6x-27=0}}}
{{{x^2-9x+3x-27=0}}}
{{{(x^2-9x)+(3x-27)=0}}}
{{{x(x-9)+3(x-9)=0}}}
{{{(x+3)(x-9)=0}}}

so, {{{(x+3)=0}}}=> if {{{x=-3}}} and {{{(x-9)=0}}}=> if {{{x=9}}}

then,  domain is:
{ {{{x}}} element {{{R}}} : {{{x<>-3}}} and {{{x<>9}}} }

 {{{drawing( 600, 600, -15, 17, -15, 15, 
line(-3,-15,-3,15),line(9,-15,9,15),
graph( 600, 600, -15, 17, -15, 15, (x^2-25)/(x^2-6x-27))) }}}