Question

Find the domain of the given function. f(x) = square root of quantity x plus eight divided by quantity x plus four times quantity x minus six.
f(x)=sqrt[x+8]/(x+4)(x-6)

Answer 1

Your f(x)=sqrt[x+8]/(x+4)(x-6) is MUCH clearer, but not 100% clear.  I will assume that your denominator here is the product of (x+4) and (x-6):

           √x+8)

f(x) = ------------------    

          (x+4)(x-6)

We cannot divide by zero.  Thus, x cannot be -4 and cannot be 6.

Thus, the domain is:

(-infinity, -4) or (-4, 6) or (6, infinity).