Question 831698
Look for values where the function is not defined. 
Example : When the denominator goes to zero, when the argument of a square root becomes negative.
In this case, you have a removable discontinuity because of the numerator.
{{{f(x)=sqrt((x-2)/(x^2-4))}}}
{{{f(x)=sqrt((x-2)/((x+2)(x-2)))}}}
{{{f(x)=sqrt(1/(x+2))}}}
So then,
{{{x^2-4=0}}}
{{{x+2=0}}}
{{{x=-2}}}
Additionally,
{{{1/(x+2)>0}}}
{{{x+2>0}}}
{{{x>-2}}}
So the domain is {{{x>-2}}}
{{{ graph( 300, 300, -10, 10, -10, 10, sqrt((x-2)/(x^2-4))) }}}