Question 992573
I'm going to assume the function is {{{f(x) = (5x^3-5)/(x^2+3x-18)}}}



Set the denominator equal to 0 and solve for x.



{{{x^2+3x-18=0}}}



{{{(x+6)(x-3)=0}}}



{{{x+6=0}}} or {{{x-3=0}}}



{{{x=-6}}} or {{{x=3}}}



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If {{{x=-6}}} or {{{x=3}}}, then {{{x^2+3x-18=0}}}



To avoid division by zero, we exclude those values out of the domain. Any other x value is allowed.



Draw out a number line. Plot -6 and 3 on it. Those values will have open holes at them because we're excluding them from the domain.



So that means the answer in interval notation is *[Tex \Large (-\infty, -6) \cup (-6,3) \cup (3,\infty)]