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!