What real values of $x$ are not in the domain of $f(x)=\frac{1}{|x^2+3x-4|+|x^2+9x+20|}$?
Let's find the values of x that ARE in the domain.
Factoring would give sqrt(x-4)(x+1)
x=4
x=-1
Therefore, the values of x that are NOT in the domain would be everything minus x=4 and x=-1.
That would give us (-infinity, -1) U (4, infinity).
Hope this helped!