Simplify the expression

f(x) = (3-sqrt(x)) / (x-9)

If g(x) was the result of the simplification, would the domains be the same?

(3-√x) / (x-9)
multiply both the numerator and denominator by (3+√x) we get,
[(3-√x)(3+√x)]/ (x-9)(3+√x)
=[3^2-(√x)^2]/(x-9)(3+√x)
=(9-x)/(x-9)(3+√x)
=-(x-9)/(x-9)(3+√x)
=-1/(3+√x)
This is the simplified form of f(x)

Multiply by the conjugate.

I.e, multiply the function by (3+sqrt(x)) / (3+sqrt(x)).

I'm not sure what the answer is, but that should simplify it.

The domain will probably not be the same. In f(x), the domain is all real numbers except that x does not equal 9. g(x) may not have the same issue.