Question 933429
I think you mean,
{{{g(x)=(2x)/(x^2-9)=(2x)/((x-3)(x+3))}}}
Look for the points where the denominator goes to zero, these points are excluded from the domain since division by zero is undefined.
{{{x-3=0}}}
{{{x=3}}}
and
{{{x+3=0}}}
{{{x=-3}}}
So then in interval notation,
Domain : ({{{infinity}}},{{{-3}}})U({{{-3}}},{{{3}}})U({{{3}}},{{{infinity}}})