Question 893024
That should really be {{{g(x)= (x+5)/(x^2+49x)}}}.


The domain of g(x) is the set of values which are acceptable for x.
The numerator presents no restrictions.  Look next at the denominator.


{{{x^2+49x=x(x+49)}}}.  This must not be allowed to be zero because a denominator can never be zero.
This expression, the denominator, will be zero for x=0 or for x=-49.  The domain then is the real
numbers such that {{{highlight(x<>0)}}} AND {{{highlight(x<>-49)}}}.


DOMAIN:  {{{-infinity<x<-49}}} U {{{-49<x<0}}} U {{{0<x<infinity}}}