For what value(s) of x does the graph of g(x) = x+10/x^3+5x^2-50x have a hole?
Anywhere the denominator = 0 there will be a hole
x=0 produces a denominator = 0 so that is one hole....
now you try x= 10 and -10 to see if denominator = 0 , another hole
Factor (if necessary) both the numerator and the denominator of the function.
If you have a term in the numerator which cancels a term in the denominator, then there will be a hole where
this term becomes zero.
For instance, if the function is: f(x) = [ (x + 6)(x - 9) ] / [ (x + 7)(x - 9) ]
there will be a hole at x = 9 and the function reduces to f(x) = (x + 6) / (x + 7).
There won't be a hole at x = -7; here, expect a vertical asymptote.