If y/(x - z) = (y + x)/z = x/y then find z : y : x ?

Given, y/(x - z) = (y + x)/z = x/y
$yz = xy + x2 - yz - xz ....\left(1\right)$
Also $\frac{x}{y} = \frac{y}{x-z}$  $\Rightarrow x2 -xz = y2 ....\left(2\right)$
Using (1) and (2), we get yz = xy - yz + $y2$
2yz = xy + $y2$
2z = x + y
Only option (B) satisfies the equation.