g(x) = x / x^2 + x - 8

Question

^{what is the domain of this equation} 

Answer 1

You give us function g(x) = x / x^2 + x - 8and I ask what is the denominator; if it's everything that appeared following the / (division), then all of that denominator polynomial needs to be enclosed in parentheses: g(x) = x / (x^2 + x - 8).

 

If not, then the problem would have been simplifiable, e.g. g(x) = 1/ x + x - 8 and that domain would be all Reals except 0.

 

If you accept the parenthesized-denominator version, then the domain is all Reals except the zeros of the quadratic denominator. Since said denominator is NOT FACTORABLE, you'll have to find its zeros using the quadratic formula; they'll be irrational by virtue of containing the square root of the discriminant.  The discriminant is 1-4(-8) = 33.