If f(x)=2-x1/2 and g(x)=x^2-9, what is the domain of g(x) divided by f(x)

I'm assuming X1/2 is sqrt(x)=x^(1/2)=x^.5

You have to rationalize the denominator of 2-x^.5 which means multiplying by the conjugate or (2+x^.5)/(2+x^.5) which has a value of 1, so you aren't changing the value at all.
The answer is
( 3x^2 - x^2.5 -9x^.5 - 18)/(4-x)