how to solve equations like SQRT(x-6)/SQRT(4-x) for their domain

Answer 1

The domain will be all real numbers except:
where the denominator is zero
one of the radicands is negative

so,
x-6 >= 0, or x >= 6
4-x >= 0, or x <= 4
exclude x=4

we want all x satisfying all of the above. I don't see any.

x >= 6 means 4-x < 0
x < 4 means x-6 < 0

so, nowhere is there a valid sqrt possible