You can put this solution on YOUR website! 1/(x^2+7x-8)
division by zero is not allowed.
x^2+7x-8=0
(x+8)(x-1)=0
x=-8 x=1
So the domain of f(x)= all real numbers except x=-8 or x=1
If either of those 2 numbers occur the denominator turns to zero.
Check it out for yourself. Substitute one of those numbers for x.
Ed