Solve the equation for x, y and z: $\sqrt{x-y+z}=\sqrt x - \sqrt y + \sqrt z$

Solve the equation for x, y and z: $\sqrt{x-y+z}=\sqrt x - \sqrt y + \sqrt z$



I am having some trouble with this problem,

Solve for $x,y,$ and $z$. $$\sqrt{x-y+z}=\sqrt x - \sqrt y + \sqrt z$$

Here is my work so far,

$$x - y +z = x+y+z-2\sqrt{xy} + 2\sqrt{xz}- 2\sqrt{zy}$$ $$2y-2\sqrt{xy} +

2\sqrt{xz}- 2\sqrt{zy} = 0 $$ $$2(y-\sqrt{xy} + \sqrt{xz} - \sqrt{zy}) = 0

$$ $$y-\sqrt{xy} + \sqrt{xz} - \sqrt{zy} = 0$$