Range of $f(x)=\large\frac{x-[x]}{1+x-[x]}$ where $[x]$ is greatest integer function.

Question

(A) $[0,1]$

(B) $[0,\large\frac{1}{2}$$]$

(C) $[0,\large\frac{1}{2}$$)$

(D) $(0,1)$