Through which door did he enter​

(2/3 (x^2+4)^(1/2) (x^2-9)^((-2)/3)-x(x^2-9)^(1/3) (x^2+4)^((-1)/2))/(x^2+4)

The two terms in the numerator are 2/3 (x^2+4)^(1/2) (x^2-9)^((-2)/3)
and -x(x^2-9)^(1/3) (x^2+4)^((-1)/2)

Dividing the first term with the denominator (x^2+4), you get: 2/3 (x^2+4)^(-(1)/2) (x^2-9)^((-2)/3)

Dividing the second term with the denominator, you get: -x(x^2-9)^(1/3) (x^2+4)^((-3)/2)

So, combining the results(that is adding them), the answer is:

2/3 (x^2+4)^(-(1)/2) (x^2-9)^((-2)/3) -x(x^2-9)^(1/3) (x^2+4)^((-3)/2)