If $x\ \propto \ y$ and $y\ \propto \ \dfrac{1}{z}$, then which of the following is correct
$\color{green}{a.)\ x\ \propto \ z} \\ b.)\ x\ \propto \ \dfrac{1}{z}$
I did
$x=k_{1}y,\ y=\dfrac{k_{2}}{z} \\ x=\dfrac{k_{1}k_{2}}{z} \\ x=\dfrac{k_{3}}{z} \\ x\propto \dfrac{1}{z} \\ $
But the answer given in this video is $x\ \propto \ z$
I look for a short and simple way.
I have studied maths up to $12$th grade.