Question 760469
Finding and checking around critical points would be the best way.  The function is {{{f(x)=sqrt((x+2)/((x-3)(x-5)))}}}.  Critical points are x element of {-2, 3, 5}.  x is allowed to be -2, but is NOT allowed to be 3 or 5.  For the rest of finding the domain, check the intervals which the critical points create.


The intervals to check are these:
(-infin, -2]
[-2, 3)
(3, 5)
(5, infin)
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If a value in the interval makes the function true, the the interval is part of the domain; if not true, then it is excluded from the domain.