If x ≠ y ≠ z ≠ 0 , $$a^x = b^y = c^z$$ and $$\frac{a}{b} = \frac{b}{c}$$, then $$\frac{y - x}{z - y}$$ =

Let say,

$$a^x=b^y=c^z=k.$$

or,$$a=k^{\frac{1}{x}},\ b=k^{\frac{1}{y}}\ and\ c=k^{\frac{1}{z}}.$$

and $$\frac{a}{b}=\frac{b}{c}.$$

or,$$b^2=ac.$$

So,$$k^{\frac{2}{y}}=k^{\frac{1}{x}}k^{\frac{1}{y}}.$$

or,$$k^{\frac{2}{y}}=k^{\frac{1}{x}+\frac{1}{z}}.$$

or,$$\frac{2}{y}=\frac{1}{x}+\frac{1}{z}.$$

or,$$2xz=yz+xy.\ \left(multiply\ both\ side\ by\ xyz\right)$$

or,$$yz-xz=xz-xy.$$

or,$$z\left(y-x\right)=x\left(z-y\right).$$

or,$$\frac{\left(y-x\right)}{\left(z-y\right)}=\frac{x}{z}.$$

So, A is correct choice.