another solution is to find the inverse of the function and the domain of the inverse function is the range of the original function

y=2x/(x-11)

x=2y/(y-11)

x(y-11)=2y

xy-11x=2y

-11x=2y-xy

11x=-2y+xy

11x=y(x-2)

11x/(x-2)=y

y=11x/(x-2)

the domain is all real numbers except 2 so this is the range of the original function