If $z^2 = \frac{x^{1/2} + y^{1/2}}{x^{1/3} + y^{1/3}}$ then $x \frac{ \partial z}{\partial x} + y \frac{ \partial z}{ \partial y}$ is :

Question

( A ) $\frac{2}{6}$
( B ) $\frac{1}{12}z$
( C ) $\frac{2}{3}z$
( D ) $\frac{2}{5}z$