Question 519729
 {{{(x^2-3)*sqrt(x^3-x)}}}
 {{{ (x^2-3)*sqrt(x*(x^2 - 1)) }}}
In the 1st factor, {{{ x^2 - 3 }}}, x can be
any real value + or -
-----------------
Of the factor inside the square root,
{{{ x }}} cannot be between {{{0}}}
and {{{1}}}
If that is true, the factor {{{ x^2 - 1 }}},
will be negative, and the square root is 
not a real number.
----------------
As for {{{x}}} between {{{0}}} and {{{-1}}},
both of the factors under the square root
turn out to be negative, and (-) x (-) = +
so that is a real number.
The domain is
{{{ x >= 1 }}}
{{{ x <= 0 }}}
or {{{ 1 <= x <= 0 }}}