question_answer

If \[\frac{x}{(2x+y+z)}=\frac{y}{(x+2y+z)}=\frac{z}{(x+y+2z)}=k\]and \[x+y+z\ne 0,\] then find k.

A)  \[\frac{1}{3}\]                         

B)  \[\frac{1}{4}\]

C)  \[\frac{1}{2}\]                         

D)  \[\frac{1}{8}\]

E)  None of these