Question 975009
{{{ sqrt( 15x/(x^2-1) ) }}}

 
denominator cannot be equal to zero, so exclude all values of {{{x}}} that make denominator equal to zero and they are:

{{{x^2-1=0}}}=>{{{x^2=1}}}=>{{{x=1}}} or {{{x=-1}}} (asymptote)

the domain is: 

{ {{{x}}} element {{{R}}} : {{{-1<x<=0}}} or {{{x>1}}}}
(assuming a function from reals to reals)

{{{drawing( 600, 600, -10, 10, -10, 10, 
circle(-1,0,.15),circle(1,0,.15),circle(0,0,.14),
line(-1,10,-1,-10),line(1,10,1,-10),
 graph( 600, 600, -10, 10, -10, 10, sqrt( 15x/(x^2-1) ))) }}}